Preparation for Calculus II
There are many topics from precalculus used in this course and you may need to refresh your memory on these topics. The suggestestions given below are based on the following book:
Precalculus, Fifth Edition, by Stewart, Redlin, Watson.
Published by Brooks/Cole.
If you do not have access to a precalculus book, it is strongly suggested that you obtain a copy of this book for reference throughout the calculus sequence.
Cengage has kindly donated a number of copies to our math library. Some are available to check out and some are on reserve and can be consulted at the library.
The book is also available on Amazon.com both new and second hand at very reasonable prices.
You may also find information on these topics on the internet including videos on Khan Academy.
We plan to add videos to this webpage in the future.
Chapter 2: Functions
Section 2.8 will be covered briefly in calculus II, in addition to the relationship between derivatives of functions and derivatives of their inverses ( when derivatives and inverses exist). For an introductory approach to One-to-One Functions and Their Inverse, please read:
Section 2.8: One-to-One Functions and Their Inverses.
Chapter 4: Exponential and Loarithmic Functions.
Logarithmic and Exponential functions will be introduced and used throughout Calculus II. It would be wise to practice using the laws of logarithms and exponents etc... in preparation for calculus II. The following sections will be very useful for your preparation.
Section 4.1: Exponential Functions.
Section 4.2: Logarithmic Functions.
Section 4.3: Laws of Logarithms.
Section 4.4: Exponential and Logarithmic Equations.
Chapter 7: Analytic Trigonometry
Trigonometric identities will be used extensively in calculus II. Also the inverse trigonometric functions will be covered quicky in Calculus II. You will find an introduction to these in Section 7.5 of the precalculus book.
Section 7.1: Trigonometric Identities.
Section 7.2: Addition and Subtraction Formulas.
Section 7.3: Double-Angle and Half-AngleFormulas.
Section 7.4: Inverse Trigonometric Functions.
Section 7.5: Trigonometric Equations.
Chapter 3: Polynomials and Rational Functions
As in Calculus I, polynomials and rational functions are very important. Section 3.2 will become important for integration by partial fraction decomposition.
Section 3.2: Dividing Polynomials.
Chapter 9: Systems of Equations and Inequalities.
To prepare for integration of rational functions by partial fraction decomposition you should review the following sections of Chapter 9. Section 9.8 will be covered briefly in Calculus II.
Section 9.1: Systems of Equations.
Section 9.2: Systems of Linear Equations in Two variables.
Section 9.3: Systems of Linear Equations in Several variables.
Section 9.8: Partial Fractions.
Chapter 8: Polar Coordinates and Vectors
Sections 8.1 and 8.2 are included in Calculus II, but if you feel like starting with an introductory approach, you should study the following sections. Obviously in Calculus II, we also include results from calculus.
Section 8.1: Polar Coordinates.
Section 8.2: Graphs of Polar Equations.
Chapter 11: Sequences and Series
Sections 11.1, 11.2 and 11.3 are included in Calculus II, but again, if you feel likestarting with an introductory approach, you should study the following sections.
Section 11.1: Sequences and Summation Notation.
Section 11.2: Arithmetic Sequences.
Section 11.3: Geometric Sequences.