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 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 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 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: 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 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.
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.
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 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 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.