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 covers following topics of Integral and
Differential Calculus: Differential Calculus: rates of change, speed, slope of a graph, minimum
and maximum of functions, Derivatives measure instantaneous changes, Integral
Calculus: Integrals measure the accumulation of some quantity, the total
distance an object has travelled, area under a curve, volume of a region.
This book covers the following
topics: Analytic Geometry, Instantaneous Rate Of Change: The Derivative, Rules
For Finding Derivatives, Transcendental Functions, Curve Sketching, Applications
of the Derivative, Integration, Techniques of Integration, Applications of
Integration, Sequences and Series.
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.
In this book, much emphasis is put on
explanations of concepts and solutions to examples. Topics covered includes:
Sets, Real Numbers and Inequalities, Functions and Graphs, Limits,
Differentiation, Applications of Differentiation, Integration, Trigonometric
Functions, Exponential and Logarithmic Functions.
This note explains the following topics:
Functions and Their Graphs, Trigonometric Functions, Exponential Functions,
Limits and Continuity, Differentiation, Differentiation Rules, Implicit
Differentiation, Inverse Trigonometric Functions, Derivatives of Inverse
Functions and Logarithms, Applications of Derivatives, Extreme Values of
Functions, The Mean Value Theorem, Monotone Functions and the First Derivative
Test, Integration, Sigma Notation and Limits of Finite Sums, Indefinite
Integrals and the Substitution Method.
Goals of this note is to have a
good understanding of concepts of calculus and applications of calculus in
sciences and engineering. Topics covered includes: polynomials and special
functions, The Concept of Limit, Computation of Limit, Continuity and its
Consequences, Limits Involving Infinity, Tangent Lines and Velocity, Computation
of Derivatives, Derivatives of Trigonometric Functions.
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 book covers
the following topics: Field of Reals and Beyond,
From Finite to Uncountable Sets, Metric Spaces and Some Basic Topology,
Sequences and Series, Functions on Metric Spaces and Continuity, Riemann
This lecture note covers the following topics: General linear
homogeneous ODEs, Systems of linear coupled first order ODEs,Calculation of
determinants, eigenvalues and eigenvectors and their use in the solution of
linear coupled first order ODEs, Parabolic, Spherical and Cylindrical polar
coordinate systems, Introduction to partial derivatives, Chain rule, change of
variable, Jacobians with examples including polar coordinate systems, surfaces and Sketching simple quadrics.
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.