CALCULUS STUDY GUIDE (pdf)

We have combined the Calculus 1 and Calculus 2 study guides into one 12-page Calculus study guide. The topics covered in this super-sized Calculus study guide include:

• Straight lines in Cartesian coordinate planes

• Functions and graphs

• Absolute value functions

• Greatest integer functions

• Limits

• One-sided limits

• Existence of limits

• Laws of limits

• Infinite limits

• Limits at infinity

• Squeeze theorem

• Continuity

• Theorems on continuity

• Intermediate Value Theorem

• Derivatives and differentiable functions

• One-sided derivatives

• Differentiable functions

• Rules of differentiation and standard derivatives

• Derivatives of inverse functions

• Implicit differentiation

• Higher derivatives

• Parametric equations

• Mean Value Theorem

• Linear approximation

• Increasing/decreasing functions

• Concavity

• Absolute extrema

• Critical points

• Local extrema

• First derivative test for local extrema

• First derivative test for absolute extrema

• Taylor's Theorem

• L'Hopital's Rule

• Antiderivatives

• Standard integrals

• Riemann Sums and definite integrals

• Properties of definite integrals

• Trigonometric integrals

• Integration by partial fractions

• Integration by substitution

• Trigonometric substitution

• Integration by parts

• Fundamental Theorem of Calculus

• Area between curves

• Volume of solids of revolution

• Arc length

• Surface area

• Polar coordinates

• First order ordinary differential equations

About the author

Ng Wee Seng obtained a Master of Science degree in Statistics and a First-class Honours degree in Mathematics from the National University of Singapore (NUS). He is currently a lecturer at NUS. He has been teaching undergraduate courses in Mathematics and Statistics since 2001. He is the author of two university-level Mathematics text books.

Screen shot of page one out of twelve for the Calculus Study Guide (pdf)