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Calculus I - 2014 Fall

Lecturenotes

 

 

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Chapter 1 Functions and Models
1.5 Exponential Functions
1.6 Inverse Functions and Logarithms
Chapter 2 Limits and derivatives
2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws
2.4 The Precise Definition of a Limit
2.5 Continuity
2.6 Limits at Infinity; Horizontal Asymptotes
2.7 Derivatives and Rates of Change
2.8 The Derivative as a Function
Chapter 3 Differentiation Rules
3.1 Derivatives of Polynomials and Exponential Functions
3.2 The Product and Quotient Rules
3.3 Derivatives of Trigonometric Functions
3.4 The Chain Rule
3.5 Implicit Differentiation
3.6 Derivatives of Logarithmic Functions
3.9 Related Rates
3.10 Linear Approximations and Differentials
Chapter 4 Applications of Differentiation 4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem
4.3 How Derivatives Affect the Shape of a Graph
4.5 Summary of Curve Sketching
4.4 Indeterminate Forms and L’Hospital’s Rule
4.7 Optimization Problems
4.9 Antiderivatives
Chapter 5 Integrals
5.1 Areas and Distances
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus
5.4 Indefinite Integrals and the Net Change Theorem
5.5 The Substitution Rule
Chapter 6 Applications of Integration
6-1 Areas Between Curves
6.2 Volumes
6.3 Volumes by Cylindrical Shells
6.5 Average Value of a Function
Chapter 7 Techniques of Integration
7.1 Integration by Parts
7-2 Trigonometric Integrals
7-3 Trigonometric Substitution
7-4 Integration of Rational Function by Partial Fraction
7-7 Approximate Integration
7-8 Improper Integrals
8-1 Arc Length
8-2 Area of a Surface of Revolution
8-3 Applications to Physics and Engineering
8-5 Probability
Chapter 10 Parametric Equations and Polar Coordinates
10-1 Curves Defined by Parametric Equation
10-2 Curves Defined by Parametric Equation
10-3 Polar Coordinates
10.4 Area and Lengths in Polar Coordinates

 

 

 
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