Precalculus (Schaum) – Fred Safier – 1st Edition


This text reviews algebra and trigonometry and prepares students for first year calculus courses at university. It shows in simple steps how to apply the basic principles to actual problems, and is suitable for struggling students who want to master the basics before starting a university level calculus course.

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Table of Contents

1. Preliminaries
2. Polynomials
3. Exponents
4. Rational and Radical Expressions
5. Linear and Non-Linear Equations
6. Linear and Non-Linear Inequalities
7. Absolute Value in Equations and Inequalities
8. Analytic Geometry
9. Functions
10. Linear Functions
11. Transformations and Graphs
12. Quadratic Functions
13. Algebra of Functions, Inverse Functions
14. Polynomial Functions
15. Rational Functions
16. Algebraic Functions, Variation
17. Exponential Functions
18. Logarithmic Functions
19. Exponential and Logarithmic Equations
20. Trigonometric Functions
21. Graphs of Trignometric Functions
22. Angles
23. Trigonometric Identities and Equations
24. Sum, Difference, Multiple, and Half-Angle Formulas
25. Inverse Trigonometric Functions
26. Triangles
27. Vectors
28. Polar Coordinates, Parametric Equations
29. Trigonometric Form of Complex Numbers
30. Systems of Linear Equations
31. Gaussian and Gauss-Jordan Elimination
32. Partial Fraction Decomposition
33. Non-Linear Systems of Equations
34. Introduction to Matrix Algebra
35. Matrix Multiplication and Inverses
36. Determinants and Cramer's Rule
37. Loci, Parabolas
38. Ellipses and Hyperbolas
39. Rotation of Axes
40. Conic Sections
41. Sequences and Series
42. The Principle of Mathematical Induction
43. Special Sequences and Series
44. The Binomial Theorem
45. Limits, Continuity, Derivatives
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