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
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.
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.
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.
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
is intended as a one and a half term course in calculus for students who have
studied calculus in high school. It is intended to be self contained, so that it
is possible to follow it without any background in calculus, for the
This note explains the following
topics: Hyperbolic Trigonometric Functions, The Fundamental Theorem of Calculus,
The Area Problem or The Definite Integral, The Anti-Derivative, Optimization,
L'Hopital's Rule, Curve Sketching, First and Second Derivative Tests, The Mean
Value Theorem, Extreme Values of a Function, Linearization and Differentials,
Inverse Trigonometric Functions, Implicit Differentiation, The Chain Rule, The
Derivative of Trig. Functions, The Differentiation Rules, Limits Involving
Infinity, Asymptotes, Continuity, Limit of a function and Limit Laws, Rates of
Change and Tangents to Curves.
explains the following topics: Calculus is probably not the most popular course
for computer scientists. Calculus – FAQ, Real and complex numbers, Functions,
Sequences, Series, Limit of a function at a point, Continuous functions, The
derivative, Integrals, Definite integral, Applications of integrals, Improper
integrals, Wallis’ and Stirling’s formulas, Numerical integration, Function
sequences and series.
This note covers the following
topics: Numbers and Functions, Derivatives, Limits and Continuous Functions,
Graph Sketching and Max-Min Problems, Exponentials and Logarithms, The Integral,
Applications of the integral.
This lecture note explains the
following topics: Methods of integration, Taylor polynomials, complex numbers and the complex exponential, differential equations, vector geometry and
This notes contains the details about The untyped lambda calculus, The
Church-Rosser Theorem, Combinatory algebras, The Curry-Howard isomorphism,
Polymorphism, Weak and strong normalization, Denotational semantics of PCF
This book emphasizes the fundamental concepts from calculus and
analytic geometry and the application of these concepts to selected areas of
science and engineering. Topics covered includes: Sets,
Functions, Graphs and Limits, Differential Calculus, Integral Calculus,
Sequences, Summations and Products and Applications of Calculus.
Calculus Made Easy has long been the most popular calculus
primer, and this major revision of the classic math text makes the subject
at hand still more comprehensible to readers of all levels. This is a book
that explains the philosophy of the subject in a very simple manner, making
it easy to understand even for people who are not proficient in math.