This PDF book covers the following topics related to
Multivariable Calculus : Curves Defined by Parametric Equations, Tangents,
Areas, Arc Lengths, and Surface Areas, Polar Coordinates, Vectors, Dot Products,
Cross Products, Lines and Planes, Quadric Surfaces, Vector Functions and Space
Curves, Cross Products and Projections, Functions of Several Variables, Limits
and Continuity, Partial Derivatives, Tangent Planes and Differentials, The Chain
Rule, Directional Derivatives and the Gradient Vector, Maximum and Minimum
Values, Lagrange Multipliers, Double Integrals over Rectangles, Double Integrals
over General Regions, Double Integrals in Polar Coordinates, Applications of
Double Integrals, Surface Area, Triple Integrals in Cartesian, Spherical, and
Cylindrical Coordinates, Change of Variable in Multiple Integrals, Gravitational
Potential Energy, Vector Fields, Line Integrals, etc.
Author(s): Department of Mathematics, University of
California at Berkeley
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.
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 PDF book covers the following topics related to
Multivariable Calculus : Curves Defined by Parametric Equations, Tangents,
Areas, Arc Lengths, and Surface Areas, Polar Coordinates, Vectors, Dot Products,
Cross Products, Lines and Planes, Quadric Surfaces, Vector Functions and Space
Curves, Cross Products and Projections, Functions of Several Variables, Limits
and Continuity, Partial Derivatives, Tangent Planes and Differentials, The Chain
Rule, Directional Derivatives and the Gradient Vector, Maximum and Minimum
Values, Lagrange Multipliers, Double Integrals over Rectangles, Double Integrals
over General Regions, Double Integrals in Polar Coordinates, Applications of
Double Integrals, Surface Area, Triple Integrals in Cartesian, Spherical, and
Cylindrical Coordinates, Change of Variable in Multiple Integrals, Gravitational
Potential Energy, Vector Fields, Line Integrals, etc.
Author(s): Department of Mathematics, University of
California at Berkeley
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: 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.
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.
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: 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.
These
notes are not intended as a textbook. It is hoped however that they will
minimize the amount of note taking activity which occupies so much of a
student’s class time in most courses in mathmatics. Topics covered includes: The
Real Number system & Finite Dimensional Cartesian Space, Limits, Continuity, and
Differentiation, Riemann Integration, Differentiation of Functions of Several
Variables.
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 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