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PART 1. ELEMENTARY METHODS, DIFFERENTIATION, COMPLEX NUMBERS; 1: Standard functions and techniques; 2: Differentiation; 3: Further techniques for differentiation; 4: Applications of differentiation; 5: Taylor series and approximations; 6: Complex numbers; PART 2. MATRIX AND VECTOR ALGEBRA; 7: Matrix algebra; 8: Determinants; 9: Elementary operations with vectors; 10: The scalar product; 11: Vector product; 12: Linear algebraic equations; 13: Eigenvalues and eigenvectors; PART 3. INTEGRATION AND DIFFERENTIAL EQUATIONS; 14: Antidifferentiation and area; 15: The definite and indefinite integral; 16: Applications involving the integral as a sum; 17: Systematic techniques for integration; 18: Unforced linear differential equations with constant coefficients; 19: Forced linear differential equations; 20: Harmonic functions and the harmonic oscillator; 21: Steady forced oscillations: phasors, impedance, transfer functions; 22: Graphical, numerical, and other aspects of first-order equations; 23: Nonlinear differential equations and the phase plane; PART 4. TRANSFORMS AND FOURIER SERIES; 24: The Laplace transform; 25: Laplace and z transforms: applications; 26: Fourier series; 27: Fourier transforms; PART 5. MULTIVARIABLE CALCULUS; 28: Differentiation of functions of two variables; 29: Functions of two variables: geometry and formulae; 30: Chain rules, restricted maxima, coordinate systems; 31: Functions of any number of variables; 32: Double integration; 33: Line integrals; 34: Vector fields: divergence and curl; PART 6. DISCRETE MATHEMATICS; 35: Sets; 36: Boolean algebra: logic gates and switching functions; 37: Graph theory and its applications; 38: Difference equations; PART 7. PROBABILITY AND STATISTICS; 39: Probability; 40: Random variables and probability distributions; 41: Descriptive statistics; PART 8. PROJECTS; 42: Applications projects using symbolic computing; Self-tests: selected answers; Answers to selected problems; Appendices; Further reading; Index

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