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.
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
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 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.
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.
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 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.
This note
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.
The approach followed is quite
different from that of standard calculus texts. We use natural, but occasionally
unusual, definitions for basic concepts such as limits and tangents. Topics
covered includes: Sets: Language and Notation, The Extended Real Line, Suprema,
Infima, Completeness, Neighborhoods, Open Sets and Closed Sets, Trigonometric
Functions, Continuity, The Intermediate Value Theorem, Inverse Functions,
Tangents, Slopes and Derivatives, Derivatives of Trigonometric Functions, Using
Derivatives for Extrema, Convexity, Integration Techniques.
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
Stieltjes Integration.
This lecture note explains the
following topics: Methods of integration, Taylor polynomials, complex numbers and the complex exponential, differential equations, vector geometry and
parametrized curves.
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.