Calculus 1 Summary Notes
[Chapter 1. FOUNDATION FOR CALCULUS: FUNCTIONS & LIMITS]
1.1 Functions and Change
1.2 Exponential Functions
1.3 New Functions from Old
1.4 Logarithmic Functions
1.5 Trigonometric Functions
1.6 Powers, Polynomials, and Rational Functions
1.7 Introduction to Limits and Continuity
1.8 Extending the Idea of a Limit
[Chapter 2. KEY CONCEPT: THE DERIVATIVE]
2.1 How Do We Measure Speed?
2.2 The Derivative at a Point
2.3 The Derivative Function
2.4 Interpretations of the Derivative
2.5 The Second Derivative
2.6 Differentiability
[Chapter 3. SHORT-CUTS TO DIFFERENTIATION]
3.1 Powers and Polynomials
3.2 The Exponential Function
3.3 The Product and Quotient Rules
3.4 The Chain Rule
3.5 The Trigonometric Functions
3.6 The Chain Rule and Inverse Functions
3.7 Implicit Functions
3.9 Linear Approximation and the Derivative
3.10 Theorems About Differentiable Functions
[Chapter 4. USING THE DERIVATIVES]
4.1 Using First and Second Derivatives
4.2 Optimization
4.3 Optimization and Modeling
4.4 Families of Functions and Modeling
4.5 Application to Marginality
4.6 Rates and Related Rates
[Chapter 5. THE DEFINITE INTEGRAL]
5.1 How Do We Measure Distance Traveled?
5.2 The Definite Integral
5.3 The Fundamental Theorem and Interpretations
5.4 Theorems about Definite Integrals
[Chapter 6. CONSTRUCTING ANTIDERIVATIVE]
6.1 Antiderivatives Graphically and Numerically
6.2 Constructing Antiderivatives Analytically
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