Calculus I

Table of Contents

Week 1 - Functions and Inverse

1. ⇒ Fundamental Concepts
2. ⇒ Definition of a Function
3. ⇒ Domain and Range of a Function
4. ⇒ Composition of Functions
5. ⇒ The Inverse Function and Invertibility
6. ⇒ Inverse of Trigonometric Functions
7. ⇒ Composition of Inverse Trigonometric Values

Week 2 - Differentiation

1. ⇒ Fundamental Concepts
2. ⇒ Introduction to Derivatives
3. ⇒ Differentiation Rules
4. ⇒ Implicit Differentiation
5. ⇒ Derivatives of Inverse Trigonometric Functions

Week 3 - Approximations

1. ⇒ Fundamental Concepts
2. ⇒ Approximating Function Values
3. ⇒ Linearization
4. ⇒ Differentials
5. ⇒ Taylor Polynomials
6. ⇒ Taylor’s Inequality

Week 4 - Limits

1. ⇒ Fundamental Concepts
2. ⇒ Horizontal Asymptotes
3. ⇒ Application of Asymptotes and Growth Rates
4. ⇒ Computation Rules and Standard Limits
5. ⇒ Dominance
6. ⇒ Squeeze Theorem

Week 5 - Integrals

1. ⇒ Fundamental Concepts
2. ⇒ Introduction to Integrals
3. ⇒ Computation Rules
4. ⇒ Fundamental Theorem of Calculus
5. ⇒ Substitution
6. ⇒ Integrating by Parts
7. ⇒ Approximating using Taylor’s Polynomials
8. ⇒ Unbounded Domains

Week 6 - Differential Equations

1. ⇒ Fundamental Concepts
2. ⇒ Introduction to Differential Equations
3. ⇒ Direction Fields
4. ⇒ Separable Differential Equations
5. ⇒ First Order Linear Differential Equations
6. ⇒ Linear Second Order Differential Equations
7. ⇒ Homogeneous Second Order Linear Differential Equations with Constant Coefficients
8. ⇒ Context Example for Non-Homogeneous Equations
9. ⇒ Method of Undetermined Coefficients
10. ⇒ Approximation by Taylor Polynomials