Lecture notes in Introductory Calculus

First Semester Calculus Lecture Notes

This note covers Numbers and Functions, Derivatives 1, Limits and Continuous Function, Derivatives 2, Graph Sketching and Max Min Problems, Exponentials and Logarithms, The Integral and Applications of the integral.

Author(s): NA

134 Pages

Calculus Volume 1 by Edwin Herman

This PDF book covers the following topics related to Calculus : Functions and Graphs, Limits, Derivatives, Applications of Derivatives, Integration, Applications of Integration.

Author(s): Edwin Jed Herman, University of Wisconsin-stevens Point, Gilbert Strang, Massachusetts Institute of Technology

875 Pages

Single Variable Calculus MIT

This book explains the following topics: Derivatives, Derivatives, slope, velocity, rate of change, Limits, continuity, Trigonometric limits, Derivatives of products, quotients, sine, cosine, Chain rule, Higher derivatives, Implicit differentiation, inverses, Exponential and log, Logarithmic differentiation, hyperbolic functions, Applications of Differentiation, Linear and quadratic approximations ,Curve sketching, Max-min problems, Newton’s method and other applications, Mean value theorem, Inequalities, Differentials, antiderivatives, Differential equations, separation of variables, Integration, Techniques of Integration.

Author(s): Prof. David Jerison, Massachusetts Institute of Technology

NA Pages

Exercises and Problems in Calculus

This is a set of exercises and problems for a standard beginning calculus. A fair number of the exercises involve only routine computations, many of the exercises and most of the problems are meant to illuminate points that in my experience students have found confusing.

Author(s): John M. Erdman

374 Pages

A Brief Introduction to Calculus

These notes are intended as a brief introduction to some of the main ideas and methods of calculus. Topics covered includes: Functions and Graphs, Linear Functions, Lines, and Linear Equations, Limits, Continuity, Linear Approximation, Introduction to the Derivative, Product, Quotient, and Chain Rules, Derivatives and Rates, Increasing and Decreasing Functions, Concavity, Optimization, Exponential and Logarithmic Functions, Antiderivatives, Integrals.

Author(s): NA

69 Pages

Calculus with Theory Lecture Notes

This note emphasizes careful reasoning and understanding of proofs. It assumes knowledge of elementary calculus. Topics covered includes: Integers and exponents, Square roots, and the existence of irrational numbers, The Riemann condition, Properties of integrals, Integrability of bounded piecewise-monotonic functions, Continuity of the square root function, Rational exponents, The fundamental theorems of calculus, The trigonometric functions, The exponential and logarithm functions, Integration, Taylor's formula, Fourier Series.

Author(s): Christine Breiner

NA Pages

Lecture Notes for Math by Dr. Vitaly A. Shneidman

This note covers following topics: Continuity and Limits, Continuous Function, Derivatives, Derivative as a function, Differentiation rules, Derivatives of elementary functions, Trigonometric functions, Implicit differentiation, Inverse Functions, Logarithmic functions and differentiation, Monotonicity, Area between two curves.

Author(s): Dr. Vitaly A. Shneidman

163 Pages

Applied Advanced Calculus Lecture Notes by Jan Vrbik

This note explains following topics: Ordinary Differential Equations, First-Order Differential Equations, Second Order Differential Equations, Third and Higher-Order Linear ODEs, Sets of Linear, First-Order, Constant-Coefficient ODEs,Power-Series Solution, Vector Analysis, Complex Analysis, Complex Analysis, Complex Functions.

Author(s): Jan Vrbik

136 Pages