Essential Calculus
Early Transcendental
By James Stewart
This is the complete electronic book written by James Stewart in order to support the basic concepts of calculus next editions and advanced calculus. This book provide you detailed study of basics concepts of calculus. After learning all these concepts, you would be able to solve advance calculus.
In this book, you will learn:
Functions and Limits (catalog of functions, Limit of a function, Calculating limits, Continuity, Limits involving infinity)
Derivatives (Rate of changes, Derivative as a function, Basic Formulas, Chain Rule, Implicit Differentiation, Related Rates, Linear approximation and differentials)
Inverse Functions (Exponential derivative, Exponential growth and decay, Hyperbolic functions, Logarithmic and Inverse Trigonometric Functions Indeterminate forms and L'Hospital Rules)
Applications of Derivations (Maximum and Minimum Values, Mean value Theorem, derivatives and shapes of Graphs, Curve Sketching, Optimization problems, Newtons's methods , Anti Derivatives)
Integrals (Areas and distances, Definite integrals, evaluating definite integrals, fundamental theorem of calculus, substitution rule)
Techniques of Integration (Integration by Parts, Trigonometric integrals and substitutions, Partial Fractions, Integration with tables and computer algebra system, Approximate Integration, Improper Integrals)
Application of Integration (Area between curves, Volumes by cylindrical shells, arc length, Applications to physics and Engineering, Differential Equations)
Series (Sequence, Integral and Comparison Test, Other convergence test, power Series, Representing Functions as power series, Taylor and Maclaurin Series, Applications of Taylor Polynomials)
Parametric Equations and Polar Coordinates (Parametric Curves, Calculus with parametric Curves, Areas and length in Polar coordinates, conic sections in polar coordinates)
Vectors and Geometry of Space ( Three dimensional coordinates system, the dot product, the cross product, equation s of Lines and Plans, cylinders and Quadratic Surfaces, vector functions and space curves, Arc length and curvature, motion in space, Velocity and Acceleration)
Partial Derivatives (Functions of Several variables, Tangent plans and linear Approximations, The chain rule, Directional derivatives and Gradient vectors, Lagrange multipliers)
Multiple Integrals (Double integrals over rectangles, over general regions, in polar coordinates, application of double integrals, triple integrals, Change of variable in multiple integrals)
Vector Calculus (vector fields, Fundamental theorem of line integrals, Greens theorem, Curl and divergence, parametric surfaces and their areas, stokes theorem and the divergence theorem)
Trigonometry, Proofs, Sigma Notations, The Logarithms defined as an Integral, Answer to odd number exercise.
0 comments:
Post a Comment