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Precalculus - Sample Problems 22 - Concepts from Calculus

Precalculus - Sample Problems 22 - Concepts from Calculus

Precalculus - Sample Problems 21 - Proving Trigonometric Identities

Precalculus - Sample Problems 21 - Proving Trigonometric Identities

Precalculus - Sample Problems 20 - Using Trigonometric Identities

Precalculus - Sample Problems 20 - Using Trigonometric Identities

Precalculus - Sample Problems 19 - Applications of Trigonometry

Precalculus - Sample Problems 19 - Applications of Trigonometry

Precalculus - Sample Problems 18 - Laws of Sines and Cosines

Precalculus - Sample Problems 18 - Laws of Sines and Cosines

Precalculus - Same Problems 17 - Solving Trigonometric Equations

Precalculus - Same Problems 17 - Solving Trigonometric Equations

Precalculus - Sample Midterm Exam - Through Exponential and Logarithmic Functions

Precalculus - Sample Midterm Exam - Through Exponential and Logarithmic Functions

Precalculus - Sample Problems 16 - Inverse Trigonometric Functions

Precalculus - Sample Problems 16 - Inverse Trigonometric Functions

Precalculus - Sample Problems 15 - Phase Shift and Modeling

Precalculus - Sample Problems 15 - Phase Shift and Modeling

Precalculus - Sample Problems 14 - Graphs of Sine, Cosine, and Tangent Functions

Precalculus - Sample Problems 14 - Graphs of Sine, Cosine, and Tangent Functions

Precalculus - Sample Problems 13 - Other Trigonometric Functions

Precalculus - Sample Problems 13 - Other Trigonometric Functions

Precalculus - Sample Problems 12 - Circular Sine and Cosine

Precalculus - Sample Problems 12 - Circular Sine and Cosine

Precalculus - Sample Problems 11 - Right Angle Trigonometry

Precalculus - Sample Problems 11 - Right Angle Trigonometry

Precalculus - Sample Problems 10 - Exponential and Logarithmic Applications

Precalculus - Sample Problems 10 - Exponential and Logarithmic Applications

Precalculus - Sample Problems 09 - Exponential and Logarithmic Equations and Inequalities

Precalculus - Sample Problems 09 - Exponential and Logarithmic Equations and Inequalities

Precalculus - Sample Problems 08 - Logarithmic Functions

Precalculus - Sample Problems 08 - Logarithmic Functions

Precalculus - Sample Problems 07 - Exponential Functions

Precalculus - Sample Problems 07 - Exponential Functions

Precalculus - Sample Problems 06 - Graphs of Rational Functions

Precalculus - Sample Problems 06 - Graphs of Rational Functions

Precalculus - Sample Problems 05 - Rational Functions: holes, asymptotes, and inequalities

Precalculus - Sample Problems 05 - Rational Functions: holes, asymptotes, and inequalities

Precalculus - Sample Problems 04 - Polynomials: factoring and roots

Precalculus - Sample Problems 04 - Polynomials: factoring and roots

Precalculus - Sample Problems 03 - Polynomials

Precalculus - Sample Problems 03 - Polynomials

Precalculus - Sample Problems 02b - Powers, Roots, and Radicals

Precalculus - Sample Problems 02b - Powers, Roots, and Radicals

Precalculus - Sample Problems 02a - Composition and Inverses of Functions

Precalculus - Sample Problems 02a - Composition and Inverses of Functions

Precalculus - Sample Problems 01b - Quadratic Functions

Precalculus - Sample Problems 01b - Quadratic Functions

Precalculus - Sample Problems 01a - Linear Functions

Precalculus - Sample Problems 01a - Linear Functions

Precalculus - Lecture 22b - Concepts of Calculus Graphs and Limits

Precalculus - Lecture 22b - Concepts of Calculus Graphs and Limits

Precalculus - Lecture 22a - Concepts of Calculus: rates of change

Precalculus - Lecture 22a - Concepts of Calculus: rates of change

Precalculus - Lecture 21 - Proving Trigonometric Identities

Precalculus - Lecture 21 - Proving Trigonometric Identities

Precalculus - Lecture 20 - Using Trigonometric Identities

Precalculus - Lecture 20 - Using Trigonometric Identities

Precalculus - Lecture 19 - Applications of Trigonometry

Precalculus - Lecture 19 - Applications of Trigonometry

Precalculus - Sample Exam (through rational functions)

Precalculus - Sample Exam (through rational functions)

Precalculus - Lecture 18 - Laws of Sines and Cosines

Precalculus - Lecture 18 - Laws of Sines and Cosines

Precalculus - Lecture 17 - Solving Trigonometric Equations

Precalculus - Lecture 17 - Solving Trigonometric Equations

Precalculus - Lecture 16 - Inverse Trigonometric Functions

Precalculus - Lecture 16 - Inverse Trigonometric Functions

Precalculus - Lecture 15 - Phase Shift and Modeling

Precalculus - Lecture 15 - Phase Shift and Modeling

Precalculus - Lecture 14 - Graphs of Trigonometric Functions

Precalculus - Lecture 14 - Graphs of Trigonometric Functions

Precalculus - Lecture 13 - Other Trigonometric Functions (in circles)

Precalculus - Lecture 13 - Other Trigonometric Functions (in circles)

Precalculus - Lecture 12b - Circular Trigonometry

Precalculus - Lecture 12b - Circular Trigonometry

Precalculus - Lecture 12a - Angles

Precalculus - Lecture 12a - Angles

Exercise 2-2-9 (Real Analysis I, Jiri Lebl)

Exercise 2-2-9 (Real Analysis I, Jiri Lebl)

Precalculus - Lecture 11 - Right Angle Trigonometry

Precalculus - Lecture 11 - Right Angle Trigonometry

Precalculus - Lecture 10 - Exponential and Logarithmic Applications

Precalculus - Lecture 10 - Exponential and Logarithmic Applications

Precalculus - Lecture 09 - Exponential and Logarithmic Equations

Precalculus - Lecture 09 - Exponential and Logarithmic Equations

Precalculus - Lecture 08 - Logarithmic Functions

Precalculus - Lecture 08 - Logarithmic Functions

Exercise 1-2-10 (Real Analysis I, Jiri Lebl)

Exercise 1-2-10 (Real Analysis I, Jiri Lebl)

Precalculus - Lecture 07 - Exponential Functions

Precalculus - Lecture 07 - Exponential Functions

Precalculus - Lecture 06 - Graphing Rational Functions

Precalculus - Lecture 06 - Graphing Rational Functions

Precalculus - Lecture 05 - Rational Functions

Precalculus - Lecture 05 - Rational Functions

Precalculus - Lecture 04 - Factoring Polynomials

Precalculus - Lecture 04 - Factoring Polynomials

Precalculus - Lecture 03 - Polynomials

Precalculus - Lecture 03 - Polynomials

Precalculus - Lecture 02(b) - Power Functions and Root Functions

Precalculus - Lecture 02(b) - Power Functions and Root Functions

Precalculus - Lecture 02(a) - Composition Functions and Inverse Functions

Precalculus - Lecture 02(a) - Composition Functions and Inverse Functions

Precalculus - Lecture 01(b) - Quadratic Functions

Precalculus - Lecture 01(b) - Quadratic Functions

Precalculus - Lecture 01(a) - Linear Functions

Precalculus - Lecture 01(a) - Linear Functions

Exercise 2-1-10 (Real Analysis I, Jiri Lebl)

Exercise 2-1-10 (Real Analysis I, Jiri Lebl)

08-07 Generalized and Other Continued Fractions

08-07 Generalized and Other Continued Fractions

08-06 Quadratic Irrationals and Periodic Continued Fractions

08-06 Quadratic Irrationals and Periodic Continued Fractions

08-05 Hurwitz's Theorem on Diophantine Approximation

08-05 Hurwitz's Theorem on Diophantine Approximation

08-04 Best Approximations of the First Kind

08-04 Best Approximations of the First Kind

08-03 Best Approximations of the Second Kind

08-03 Best Approximations of the Second Kind

08-02 Regular Continued Fractions of Irrational Numbers

08-02 Regular Continued Fractions of Irrational Numbers

08-01 Regular Continued Fractions of Rational Numbers

08-01 Regular Continued Fractions of Rational Numbers

Extras-06: Gaussian Brackets

Extras-06: Gaussian Brackets

What is "Dimension"?

What is "Dimension"?

Precalculus Problem Set 22 - Concepts from Calculus

Precalculus Problem Set 22 - Concepts from Calculus

Precalculus Problem Set 21 - Proving Trigonometric Identities

Precalculus Problem Set 21 - Proving Trigonometric Identities

Precalculus Problem Set 20 - Using Trigonometric Identities

Precalculus Problem Set 20 - Using Trigonometric Identities

Precalculus Problem Set 19 - Applications of Trigonometry

Precalculus Problem Set 19 - Applications of Trigonometry

Precalculus Problem Set 18 - The Law of Sines, The Law of Cosines

Precalculus Problem Set 18 - The Law of Sines, The Law of Cosines

Precalculus Problem Set 17 - Solving Trigonometric Equations

Precalculus Problem Set 17 - Solving Trigonometric Equations

Precalculus Problem Set 16 - Inverse Sine, Cosine, and Tangent

Precalculus Problem Set 16 - Inverse Sine, Cosine, and Tangent

Precalculus Problem Set 15 - Phase Shift and Modeling

Precalculus Problem Set 15 - Phase Shift and Modeling

Precalculus Problem Set 14 - Graphs of Sine, Cosine, and Tangent

Precalculus Problem Set 14 - Graphs of Sine, Cosine, and Tangent

Precalculus Problem Set 12 - Circular Sine and Cosine

Precalculus Problem Set 12 - Circular Sine and Cosine

Precalculus Problem Set 13 - Other Trigonometric Functions

Precalculus Problem Set 13 - Other Trigonometric Functions

Precalculus Problem Set 11 - Right Triangle Trigonometry

Precalculus Problem Set 11 - Right Triangle Trigonometry

Precalculus Problem Set 10 - Exponential and Logarithmic Applications

Precalculus Problem Set 10 - Exponential and Logarithmic Applications

Precalculus Problem Set 09 - Exponential and Logarithmic Inequalities

Precalculus Problem Set 09 - Exponential and Logarithmic Inequalities

Precalculus Problem Set 08 - Logarithmic Functions

Precalculus Problem Set 08 - Logarithmic Functions

Precalculus Problem Set 07 - Exponential Functions

Precalculus Problem Set 07 - Exponential Functions

Precalculus Problem Set 06 - Graphs of Rational Functions

Precalculus Problem Set 06 - Graphs of Rational Functions

Precalculus Problem Set 05 - Rational Functions

Precalculus Problem Set 05 - Rational Functions

SQRT(2) is irrational

SQRT(2) is irrational

Trigonometry: Triangles, Circles, and Complex Numbers

Trigonometry: Triangles, Circles, and Complex Numbers

Geometric Series via Polynomial Division #maths #geometricseries #polynomials

Geometric Series via Polynomial Division #maths #geometricseries #polynomials

Precalculus Problem Set 04 - Polynomials, Factoring, and Roots

Precalculus Problem Set 04 - Polynomials, Factoring, and Roots

Precalculus Problem Set 01b - Quadratic Functions

Precalculus Problem Set 01b - Quadratic Functions

Precalculus Problem Set 03 - Polynomials

Precalculus Problem Set 03 - Polynomials

Precalculus Problem Set 01a - Linear Functions

Precalculus Problem Set 01a - Linear Functions

Precalculus Problem Set 02b - Powers, Roots, and Radicals

Precalculus Problem Set 02b - Powers, Roots, and Radicals

Precalculus Problem Set 02a - Composition and Inverses of Functions

Precalculus Problem Set 02a - Composition and Inverses of Functions

Geometric Euclidean Algorithm

Geometric Euclidean Algorithm

The Square-Cube Law

The Square-Cube Law

Completing The Square

Completing The Square

The Pythagorean Theorem

The Pythagorean Theorem

Solving a polynomial inequality

Solving a polynomial inequality

Extra Exercises 11 - Fleury's and Dijkstra's Algorithms

Extra Exercises 11 - Fleury's and Dijkstra's Algorithms

Extra Exercises 10 - Trees and Spanning Trees

Extra Exercises 10 - Trees and Spanning Trees

Extra Exercises 09 - More Graph Theory

Extra Exercises 09 - More Graph Theory

Extra Exercises 08 - Sequences and Graphs

Extra Exercises 08 - Sequences and Graphs

Introductory Trigonometry Exam Solutions

Introductory Trigonometry Exam Solutions

Extra Exercises 07 - Proof by Induction

Extra Exercises 07 - Proof by Induction

Extra Exercises 06 - Relations and Functions

Extra Exercises 06 - Relations and Functions

Extra Exercises 05 - More Set Theory

Extra Exercises 05 - More Set Theory

Extra Exercises 04 - Problems in Basic Set Theory

Extra Exercises 04 - Problems in Basic Set Theory

Extra Exercises 03 - More Proofs and Quantified Statements

Extra Exercises 03 - More Proofs and Quantified Statements

Extra Exercises 02 - Two-Column Proofs

Extra Exercises 02 - Two-Column Proofs

Extra Exercises 01 - Truth Tables

Extra Exercises 01 - Truth Tables

Numbers

Numbers

New Series - Deep Dives

New Series - Deep Dives

60 - Variation of Parameters in Systems

60 - Variation of Parameters in Systems

59 - Laplace Transforms of Nonhomogeneous Systems

59 - Laplace Transforms of Nonhomogeneous Systems

58 - Laplace Transforms of Homogeneous Systems

58 - Laplace Transforms of Homogeneous Systems

57 - Systems of Equations with Complex Eigenvalues

57 - Systems of Equations with Complex Eigenvalues

56 - Systems of Equations with Deficient Real Eigenvalues

56 - Systems of Equations with Deficient Real Eigenvalues

55 - Diagonalizable First Order Systems

55 - Diagonalizable First Order Systems

54 - Introduction to First Order Systems

54 - Introduction to First Order Systems

53 - Review of Eigenvalues and Eigenvectors

53 - Review of Eigenvalues and Eigenvectors

52 - Higher Order Power Series Solutions

52 - Higher Order Power Series Solutions

51 - Higher Order Euler Equations

51 - Higher Order Euler Equations

50 - Higher Order Variation of Parameters

50 - Higher Order Variation of Parameters

49 - Higher Order Laplace Transforms

49 - Higher Order Laplace Transforms

48 - Higher Order Undetermined Coefficients

48 - Higher Order Undetermined Coefficients

47 - Higher Order Linear Homogeneous Equations

47 - Higher Order Linear Homogeneous Equations

46 - Forcing Functions with Impulses

46 - Forcing Functions with Impulses

45 - Impulse Functions

45 - Impulse Functions

44 - Convolution and Laplace Transforms

44 - Convolution and Laplace Transforms

43 - Piecewise Continuous Forcing Functions

43 - Piecewise Continuous Forcing Functions

42 - Laplace Transforms of Piecewise Defined Functions

42 - Laplace Transforms of Piecewise Defined Functions

41 - Laplace Transforms and Solutions to Differential Equations

41 - Laplace Transforms and Solutions to Differential Equations

40 - Inverse Laplace Transforms

40 - Inverse Laplace Transforms

39 - The Laplace Transform

39 - The Laplace Transform

38 - Power Series Solutions to Second Order Euler Equations

38 - Power Series Solutions to Second Order Euler Equations

37 - Power Series Solutions (Second Order Equations)

37 - Power Series Solutions (Second Order Equations)

36 - Power Series Solutions (First Order Equations)

36 - Power Series Solutions (First Order Equations)

35 - Series Review VI (Calculus with Power Series)

35 - Series Review VI (Calculus with Power Series)

34 - Series Review V (Reindexing)

34 - Series Review V (Reindexing)

33 - Series Review IV (Taylor Series)

33 - Series Review IV (Taylor Series)

32 - Series Review III (Power Series)

32 - Series Review III (Power Series)

31 - Series Review II (Ratio and Root Tests)

31 - Series Review II (Ratio and Root Tests)

30 - Series Review I (Basic Convergence Tests)

30 - Series Review I (Basic Convergence Tests)

29 - Motion Under A Central Force

29 - Motion Under A Central Force

28 - Damped Forced Springs

28 - Damped Forced Springs

27 - Forced Undamped Springs

27 - Forced Undamped Springs

26 - Variation of Parameters in Second Order Equations

26 - Variation of Parameters in Second Order Equations

25 - Reduction of Order

25 - Reduction of Order

24 - Nohomogeneous Equations (Poly-Expo-Trig Forcing)

24 - Nohomogeneous Equations (Poly-Expo-Trig Forcing)

23 - Nonhomogeneous Equations (Expo-Trig Forcing)

23 - Nonhomogeneous Equations (Expo-Trig Forcing)

22 - Nonhomogeneous Equations (Trig Forcing)

22 - Nonhomogeneous Equations (Trig Forcing)

03 - Separable Equations

03 - Separable Equations

05-06: Examples of Solving Systems with Non-Coprime Bases

05-06: Examples of Solving Systems with Non-Coprime Bases

21 - Nonhomogeneous Equations (Exponential Forcing)

21 - Nonhomogeneous Equations (Exponential Forcing)

20 - Euler Equations with Algebraic Forcing

20 - Euler Equations with Algebraic Forcing

19 - Nonhomogeneous Equations (Polynomial Forcing)

19 - Nonhomogeneous Equations (Polynomial Forcing)

18 - Second Order Euler Equations

18 - Second Order Euler Equations

14 - Fundamental Sets of Solutions

14 - Fundamental Sets of Solutions

17 - Complex Conjugate Roots

17 - Complex Conjugate Roots

16 - One Repeated Real Root

16 - One Repeated Real Root

15 - Distinct Real Roots

15 - Distinct Real Roots

13 - Undamped Pendulums

13 - Undamped Pendulums

12 - Undamped Springs and Hooke's Law

12 - Undamped Springs and Hooke's Law

11 - Damped Acceleration (Air Resistance)

11 - Damped Acceleration (Air Resistance)

10 - Single Tank Mixing

10 - Single Tank Mixing

09 - Cooling and Heating

09 - Cooling and Heating

08 - Applications: Growth/Decay and Logistic Models

08 - Applications: Growth/Decay and Logistic Models

06 - Exact Equations

06 - Exact Equations

07 - Integrating Factors

07 - Integrating Factors

05 - Substitutions in Homogeneous Equations

05 - Substitutions in Homogeneous Equations

04 - Bernoulli Equations

04 - Bernoulli Equations

02 - Linear First-Order Inhomogeneous Equations

02 - Linear First-Order Inhomogeneous Equations

01 - Linear First-Order Homogeneous Equations

01 - Linear First-Order Homogeneous Equations

6-10 A Connection to Linear Algebra

6-10 A Connection to Linear Algebra

Extras-02: Divisibility Tricks

Extras-02: Divisibility Tricks

Extras-01: Representation of Numbers in Different Bases

Extras-01: Representation of Numbers in Different Bases

Extras-04: Computing Modular Inverses

Extras-04: Computing Modular Inverses

Extras-05: RSA Encryption

Extras-05: RSA Encryption

Extras-03: The Successive Squaring Algorithm

Extras-03: The Successive Squaring Algorithm

07-03: Primitive roots modulo prime bases

07-03: Primitive roots modulo prime bases

07-01: Order of integers modulo n

07-01: Order of integers modulo n

07-02: Primitive Roots

07-02: Primitive Roots

07-06: Find All Primitive Roots modulo n

07-06: Find All Primitive Roots modulo n

07-04: Primitive Roots modulo Prime Powers

07-04: Primitive Roots modulo Prime Powers

07-05: Primitive Roots modulo Other Bases

07-05: Primitive Roots modulo Other Bases

06-02: The Legendre Symbol

06-02: The Legendre Symbol

06-05: Examples of Using Gauss' Method

06-05: Examples of Using Gauss' Method

06-08: Examples using Quadratic Reciprocity

06-08: Examples using Quadratic Reciprocity

06-06: Eisenstein's Lemma

06-06: Eisenstein's Lemma

06-07: The Law of Quadratic Reciprocity

06-07: The Law of Quadratic Reciprocity

06-04: Gauss' Method

06-04: Gauss' Method

06-03: Euler's Method

06-03: Euler's Method

06-01: Quadratic Residues

06-01: Quadratic Residues

05-04: Examples Using the Chinese Remainder Theorem

05-04: Examples Using the Chinese Remainder Theorem

05-06: Examples of Solving Systems with Non-Coprime Bases

05-06: Examples of Solving Systems with Non-Coprime Bases

05-05: Congruences with Non-Coprime Bases

05-05: Congruences with Non-Coprime Bases

05-01: Linear congruences in one variable

05-01: Linear congruences in one variable

05-02: Two Linear Congruences

05-02: Two Linear Congruences

05-03: The Chinese Remainder Theorem

05-03: The Chinese Remainder Theorem

04-06: Fermat Primality Test and Carmichael Numbers

04-06: Fermat Primality Test and Carmichael Numbers

04-05: Modular Inverses

04-05: Modular Inverses

03-09: Sample Problems

03-09: Sample Problems