Master Math Calculus: (English)

Master Math: Calculus is an easy-to-use, informative reference for beginning students or rusty profesionals and is a welcome addition to Ross's Master Math series. Particularly effective is the presentation of topics in conjunction with practical applications. Readers will also find the first three volumes in Master Math series a useful reference because of the in-depth coverage of arithmetic, algebra, geometry, and trignometry, which provide the foundation for calculus.About the AuthorDebra Anne Ross has a double BA in Chemistry and Biology from the University of California, Santa Cruz, and an MS in Chemical Engineering from Stanford University.Table of ContentsIntroduction I Functions Functions: Types, Properties and Definitions Exponents and Logarithms Circular motion Relationship between trigonometric and exponential functions Hyperbolic functions Polynomial functions Functions of more than one variable and contour diagrams Coordinate systems Complex numbers Parabolas, Circles, Ellipses and Hyperbolas II The Derivative The Limit Continuity Differentiability The definition of the derivative and rate of change Delta notation and the definition of the derivative Slope of a tangent line and the definition of the derivative Velocity, distance, slope, and the definition of the derivative Evaluating derivatives of constants and linear functions Evaluating derivatives using the derivative formula The derivatives of a variable, a constant with a variable, a constant with function and a variable raised to a power Examples of differentiating using the derivative formula Derivatives of powers of functions Derivatives of az, ex and In x Applications oe exponential equation Differentiating sums, differences and polynomials Taking second derivatives Derivatives of products: the product rule Derivatives of quotients: the quotient rule The chain rule for differentiating complicated functions Rate problem examples Differentiating trigonometric functions Inverse functions and inverse trigonometric functions and their derivatives Differentiating hyperbolic functions Differentiating multivariable functions Differentiation of implicit vs. Explicit functions Selected rules of differentiation Minium, maximum and the first and second derivatives Notes on local linearity, approximating slope of curve and numerical methods III The Integral Introduction Sums and sigma notation The antiderivative or indefinite integral and the integral formula The definite integral and the Fundamental Theorem of Calculus Improper integrals The integral and the area under a curve Estimating integrals using sums and associated error The integral and the average value Area below the X-axis, even and odd functions and their integrals Integrating a function and a constant, the sum of functions, a polynomial, and properties of integrals Multiple integrals Examples of common integrals Integrals describing length Integrals describing area Integrals describing volume Changing Coordinates and variables Applications of the integral Evaluating integrals using integration by parts Evaluating integrals using substitution Evaluating integrals using partial fractions Evaluating integrals using tables IV Series and Approximations Sequences, progressions and series Infinite series and tests for convergence Expanding functions into series, the power series, Taylor series, Maclaurin series, and the binomial expansion V Vectors, Matrices, Curves, Surfaces and Motion Introduction to vectors Introduction to matrices Multiplication of vectors and matrices Dot or scalar products Vector or cross product Summary of determinants Matrices and linear algebra The position vector, paramteric equations, curves and surfaces Motion, velocity and acceleration VI Partial Derivatives Partial Derivatives: Representation and Evaluation The chain rule Representation on a graph Local linearity, linear approximations, quadratic approximations and differentials Directional derivative and gradient Minima, maxima and optimization VII Vector Calculus Summary of scalars, vectors, the directional derivatives and the gradient Vector fields and field lines Line integrals and conservative vector fields Green's Theorem: Tangent and Normal (flux) forms Surface integrals and flux Divergence Curl Stokes' Theorem VIII Introduction to Differential Equations First-order differential equations Second-order linear differential equations Higher-order linear differential equations Series solutions to diffential equations Systems of differential equations Laplace transform method Numerical methods for solving differential equations Partial differential equations Index