Master Math · Pre-Calculus by Ross, Debra Anne -- Read -- Imperial Library of Trantor

Index

1.1. Lines and Angles 1.2. Polygons 1.3. Triangles 1.4. Quadrilaterals (Four-Sided Polygons) 1.5. Circles 1.6. Perimeter and Area of Planar Two-Dimensional Shapes

Triangle Square Rectangle Regular Hexagon Circle Triangle Square Rectangle Parallelogram Trapezoid Circle

1.7. Volume and Surface Area of Three-Dimensional Objects 1.8. Vectors

2. Trigonometry

2.1. Introduction 2.2. General Trigonometric Functions 2.3. Addition, Subtraction, and Multiplication of Two Angles 2.4. Oblique Triangles

Law of Sines Law of Cosines Law of Tangents

2.5. Graphs of Cosine, Sine, Tangent, Secant, Cosecant, and Cotangent 2.6. Relationship Between Trigonometric and Exponential Functions 2.7. Hyperbolic Functions

3. Sets and Functions

3.1. Sets 3.2. Functions

4. Sequences, Progressions, and Series

4.1. Sequences 4.2. Arithmetic Progressions 4.3. Geometric Progressions 4.4. Series 4.5. Infinite Series: Convergence and Divergence 4.6. Tests for Convergence of Infinite Series

The Comparison Test for Convergence The Ratio Test for Convergence Tests for Series with Positive and Negative Terms Integral Test for Convergence

4.7. The Power Series 4.8. Expanding Functions into Series 4.9. The Binomial Expansion

5. Limits

5.1. Introduction to Limits 5.2. Limits and Continuity

6. Introduction to the Derivative

6.1. Definition 6.2. Evaluating Derivatives 6.3. Differentiating Multivariable Functions 6.4. Differentiating Polynomials 6.5. Derivatives and Graphs of Functions 6.6. Adding and Subtracting Derivatives of Functions 6.7. Multiple or Repeated Derivatives of a Function 6.8. Derivatives of Products and Powers of Functions 6.9. Derivatives of Quotients of Functions 6.10. The Chain Rule for Differentiating Complicated Functions 6.11. Differentiation of Implicit vs. Explicit Functions 6.12. Using Derivatives to Determine the Shape of the Graph of a Function (Minimum and Maximum Points)

Minimum and Maximum Points

6.13. Other Rules of Differentiation 6.14. An Application of Differentiation: Curvilinear Motion

7. Introduction to the Integral

Area of Functions That Extend Below the X-Axis

7.6. Integrals and Volume 7.7. Even Functions, Odd Functions, and Symmetry 7.8. Properties of the Definite Integral 7.9. Methods for Evaluating Complex Integrals: Integration by Parts, Substitution, and Tables

Integral Tables