Calculus

Calculus

If you do not understand your existing textbook then this is an excellent book to start reading.

Contents

• Rates of Change: Change in discrete steps, Two sides of the same coin, Some guesses
• Continuous change: A derivative, Properties of the derivative, Higher-order polynomials, The second derivative, Maxima and minima
• Infinity and beyond! Infinitesimals, Safe use of infinitesimals, The product rule, The chain rule, Exponentials and logarithms, The exponential, The logarithm, Quotients, Differentiation on a computer, Continuity, Limits, L’H opital’s rule, Another perspective on indeterminate forms.
• Integration: Definite and indefinite integrals, The fundamental theorem of calculus, Properties of the integral, Applications, Averages, Work, Probability.
• Techniques: Newton’s method, Implicit differentiation, Taylor series, Methods of integration, Change of variable, Integration by parts, Partial fractions
• Complex number techniques: Review of complex numbers, Euler’s formula, Partial fractions revisited.
• Improper integrals: Integrating a function that blows up, Limits of integration at infinity.
• Iterated integrals: Integrals inside integrals, Applications, Polar coordinates, Spherical and cylindrical coordinates

Calculus II for Dummies

A comprehensive overview of Calculus II along with an in depth review of Calculus I. Mahobe recommends this book to anyone taking a Calculus class unless they happen to be an absolute math genius. Even then we are sure that the geniuses will get a kick out of the humor interlaced through out the book.

Contents of the Book:

Part I: Introduction to Integration

• Chapter 1: An Aerial View of the Area Problem
• Chapter 2: Dispelling Ghosts from the Past: A Review of Pre-Calculus and Calculus I
• Chapter 3: From Definite to Indefinite: The Indefinite Integral

Part II: Indefinite Integrals

• Chapter 4: Instant Integration: Just Add Water (And C)
• Chapter 5: Making a Fast Switch: Variable Substitution
• Chapter 6: Integration by Parts
• Chapter 7: Trig Substitution: Knowing All the (Tri)Angles
• Chapter 8: When All Else Fails: Integration with Partial Fractions

Part III: Intermediate Integration Topics

• Chapter 9: Forging into New Areas: Solving Area Problems
• Chapter 10: Pump up the Volume: Using Calculus to Solve 3-D Problems

Part IV: Infinite Series

• Chapter 11: Following a Sequence, Winning the Series
• Chapter 12: Where Is This Going? Testing for Convergence and Divergence
• Chapter 13: Dressing up Functions with the Taylor Series

Part V: Advanced Topics

• Chapter 14: Multivariable Calculus
• Chapter 15: What’s So Different about Differential Equations?

Part VI: The Part of Tens

• Chapter 16: Ten “Aha!” Insights in Calculus II
• Chapter 17: Ten Tips to Take to the Test