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Lecture notes in Introductory Calculus
This note covers the following topics: Real Numbers,Complex numbers, Sequences and their limits, Limits and Continuity, Differentiation, Applications of Differentiation, Primitives and Indefinite Integrals.
Author(s): Department of Higher Mathematics, MIPT
310 Pages
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
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
Calculus, Applications and Theory
This note covers following topics: The Real Numbers, Basic Geometry And Trigonometry, The Complex Numbers, Functions Of One Variable, Derivatives, Properties And Applications Of Derivatives, Antiderivatives And Differential Equations, The Integral, Infinite Series, Vector Valued Functions, Limits And Derivatives, Line Integrals, Functions Of More Than One Variable, Linear Algebra, Vector Calculus.
Author(s): Kenneth Kuttler
635 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
