Abstract
COMPLEX NUMBERS. Introducing Complex Numbers. Polar Representation of Complex Numbers. Demoivrea s Theorem and Complex Algebra. VECTOR ALGEBRA. Scalar Products of Vectors. Vector Products of Vectors. DETERMINANTS AND MATRICES. Determinants. Matrices. DIFFERENTIATION, EXPANSION AND APPROXIMATION. Expansions and Approximations. Taylor Expansions and Polynomial Approximations. Hyperbolic Functions and Differentiation. INTEGRATION, SUMMATION AND AVERAGING. Areas, Volumes and Averages. Special Integration Techniques. DIFFERENTIAL EQUATIONS. Formulating and Classifying Differential Equations. Solving First--Order Differential Equations. Solving Second--Order Differential Equations. Waves and Partial Differential Equations. VECTOR CALCULUS. Differentiating Vectors. Integrating Vectors. Appendix. Answers and Comments. Index.
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