Calculus PPT PDF NOTES

Calculus Lecture Notes

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 Gold Notes 

0. Mathematical Sign Language
1. Induction
2. Polynomials and Rational Functions
3. The Mean Value Theorem for Rational Functions
4. Approximation of Rational Functions
5. Solving Polynomial Equations
6. Asymptotic Behaviour of Rational Functions
7. Taylor Approximation
8. Complex Numbers
9. Gold Problems
10. 
    

 Redbook Notes 

0. Review Notes
1. Functions
2. Limits and Continuity
3. Techniques of Differentiation
4. Related Rates
5. Rolle's Theorem, the Mean Value Theorem, and L'Hopital's Rule
6. Graph Sketching
7. Estimating Functions
8. Applications of Maxima and Minima
9. Newton's Method
10. The Definite Integral
11. Techniques of Integration
12. Applications of the Definite Integral
13. Numerical Integration
14. Taylor's Theorem
15. Differential Equations
16. 
    

 Old Tests and Exams

• 1994/95 Term Test I
• 1994/95 Term Test II
• 1994/95 Final Exam
• 1995/96 Term Test I
• 1995/96 Term Test II
• 1995/96 Final Exam
• 1996/97 Term Test I
• 1996/97 Term Test II
• 1996/97 Final Exam
• 1997/98 Term Test I
• 1997/98 Term Test II
• 1997/98 Final Exam
• 1998/99 Term Test I
• 1998/99 Term Test II
• 1998/99 Final Exam
• 1999/2000 Term Test I
• 1999/2000 Term Test II
• 1999/2000 Final Exam
• 2000/2001 Term Test I
• 2000/2001 Term Test II
• 2000/2001 Final Exam
• 2001/2002 Term Test I
• 2001/2002 Term Test II
• 2001/2002 Final Exam
• 2002/2003 Term Test I
• 2002/2003 Term Test II

Calculus PPT PDF SLIDES

Calculus Class Notes 

Copies of the classnotes are on the internet in PDF and Postscript formats as given below. I have included versions with both color figures and black and white figures (the "black and white" files are roughly 1/3 the size of the "color" files).


Files with Black and White Figures (or No Figures at All)Chapter 1: Limits and Continuity.

• Section 1-1: Rates of Change and Limits. PDF. PS.
• Section 1-2: Finding Limits and One-Sided Limits. PDF. PS.
• Section 1-3: Limits Involving Infinity. PDF. PS.
• Section 1-4: Continuity. PDF. PS.
• Section 1-5: Tangent Lines. PDF. PS.
• Study Guide. PDF. PS.

Chapter 2: Derivatives.

• Section 2-1: The Derivative as a Function. PDF. PS.
• Section 2-2: The Derivative as a Rate of Change. PDF. PS.
• Section 2-3: Derivatives of Products, Quotients, and Negative Powers. PDF. PS.
• Section 2-4: Derivatives of Trigonometric Functions. PDF. PS.
• Section 2-5: The Chain Rule and Parametric Equations. PDF. PS.
• Section 2-6: Implicit Differentiation. PDF. PS.
• Section 2-7: Related Rates. PDF. PS.
• Study Guide. PDF. PS.

Chapter 3: Applications of Derivatives.

• Section 3-1: Extreme Values of Functions. PDF. PS.
• Section 3-2: The Mean Value Theorem and Differential Equations. PDF. PS.
• Section 3-3: The Shape of a Graph. PDF. PS.
• Section 3-4: Graphical Solutions of Autonomous Differential Equations. PDF. PS.
• Section 3-5: Modeling and Optimization. PDF. PS.
• Section 3-6: Linearization and Differentials. PDF. PS.
• Section 3-7: Newton's Method. PDF. PS.
• Study Guide. PDF. PS.

Chapter 4: Integration.

• Section 4-1: Indefinite Integrals, Differential Equations and Modeling. PDF. PS.
• Section 4-2: Integral Rules; Integration by Substitution. PDF. PS.
• Section 4-3: Estimating with Finite Sums. PDF. PS.
• Section 4-4: Riemann Sums and Definite Integrals. PDF. PS.
• Section 4-5: The Mean Value and Fundamental Theorems. PDF. PS.
• Section 4-6: Substitution in Definite Integrals. PDF. PS.
• Section 4-7: Numerical Integration. PDF. PS.
• Study Guide. PDF. PS.

Chapter 5: Applications of Integrals.

• Section 5-1: Volumes by Slicing and Rotation About an Axis. PDF. PS.
• Section 5-2: Modeling Using Cylindrical Shells. PDF. PS.
• Section 5-3: Lengths of Plane Curves. PDF. PS.
• Study Guide. PDF. PS.

Chapter 5: Applications of Integrals.

• Section 5.4: Springs, Pumping, and Lifting. PDF. PS.
• Section 5.5: Fluid Forces. PDF. PS.
• Section 5.6: Moments and Centers of Mass. PDF. PS.

Chapter 6: Transcendental Functions and Differential Equations.

• Section 6.1: Logarithms. PDF. PS.
• Section 6.2: Exponential Functions. PDF. PS.
• Section 6.3: Derivatives of Inverse Trigonometric Functions; Integrals. PDF. PS.
• Section 6.4: First-Order Seperable Differential Equations. PDF. PS.
• Section 6.5: Linear First-Order Differential Equations. PDF. PS.
• Section 6.6: Euler's Method: Population Models. PDF. PS.
• Section 6.7: Hyperbolic Functions. PDF. PS.

Chapter 7: Integration Techniques, L'Hopital's Rule, and Improper Integrals.

• Section 7.1: Basic Integration Formulas. PDF. PS.
• Section 7.2: Integration by Parts. PDF. PS.
• Section 7.3: Partial Fractions. PDF. PS.
• Section 7.4: Trigonometric Substitution. PDF. PS.
• Section 7.5: Integral Tables, Computer Algebra Systems, and Monte Carlo Integration. PDF. PS.
• Section 7.6: L'Hopital's Rule. PDF. PS.
• Section 7.7: Improper Integrals. PDF. PS.

Chapter 8: Infinite Series.

• Section 8.1: Limits of Sequences of Numbers. PDF. PS.
• Section 8.2: Subsequences, Bounded Sequences, and Picard's Method. PDF. PS.
• Section 8.3: Infinite Series. PDF. PS.
• Section 8.4: Series of Nonnegative Terms. PDF. PS.
• Section 8.5: Alternating Series, Absolute and Conditional Convergence. PDF. PS.
• Section 8.6: Power Series. PDF. PS.
• Section 8.7: Taylor and Maclaurin Series. PDF. PS.
• Section 8.8: Applications of Power Series. PDF. PS.
• Section 8.9: Fourier Series. PDF. PS.
• Section 8.10: Fourier Cosine and Sine Series. PDF. PS.

Files with Color FiguresChapter 1: Limits and Continuity.

• Section 1-1: Rates of Change and Limits. PDF. PS.
• Section 1-2: Finding Limits and One-Sided Limits. PDF. PS.
• Section 1-3: Limits Involving Infinity. PDF. PS.
• Section 1-4: Continuity. PDF. PS.
• Section 1-5: Tangent Lines. PDF. PS.

Chapter 3: Applications of Derivatives.

• Section 3-2: The Mean Value Theorem and Differential Equations. PDF. PS.
• Section 3-7: Newton's Method. PDF. PS.

Chapter 4: Integration.

• Section 4-4: Riemann Sums and Definite Integrals. PDF. PS.
• Section 4-5: The Mean Value and Fundamental Theorems. PDF. PS.
• Section 4-6: Substitution in Definite Integrals. PDF. PS.
• Section 4-7: Numerical Integration. PDF. PS.

Chapter 5: Applications of Integrals.

• Section 5-1: Volumes by Slicing and Rotation About an Axis. PDF. PS.
• Section 5-2: Modeling Using Cylindrical Shells. PDF. PS.
• Section 5-3: Lengths of Plane Curves. PDF. PS.

Chapter 5: Applications of Integrals.

• Section 5.5: Fluid Forces. PDF. PS.
• Section 5.6: Moments and Centers of Mass. PDF. PS.

Chapter 6: Transcendental Functions and Differential Equations.

• Section 6.1: Logarithms. PDF. PS.
• Section 6.2: Exponential Functions. PDF. PS.
• Section 6.3: Derivatives of Inverse Trigonometric Functions; Integrals. PDF. PS.
• Section 6.5: Linear First-Order Differential Equations. PDF. PS.
• Section 6.6: Euler's Method: Population Models. PDF. PS.
• Section 6.7: Hyperbolic Functions. PDF. PS.

Chapter 7: Integration Techniques, L'Hopital's Rule, and Improper Integrals.

• Section 7.2: Integration by Parts. PDF. PS.
• Section 7.5: Integral Tables, Computer Algebra Systems, and Monte Carlo Integration. PDF. PS.
• Section 7.7: Improper Integrals. PDF. PS.

Chapter 8: Infinite Series.

• Section 8.1: Limits of Sequences of Numbers. PDF. PS.
• Section 8.2: Subsequences, Bounded Sequences, and Picard's Method. PDF. PS.
• Section 8.4: Series of Nonnegative Terms. PDF. PS.
• Section 8.5: Alternating Series, Absolute and Conditional Convergence. PDF. PS.
• Section 8.7: Taylor and Maclaurin Series. PDF. PS.
• Section 8.9: Fourier Series. PDF. PS.