Schaum's outline of theory and problems of advanced calculus:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
McGraw-Hill
1974
|
| Edition: | Si(metric) ed. |
| Series: | Schaum's outline series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 384 S. graph. Darst. |
| ISBN: | 0070843805 |
Staff View
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| 245 | 1 | 0 | |a Schaum's outline of theory and problems of advanced calculus |c by Murray R. Spiegel |
| 246 | 1 | 3 | |a Theory and problems of advanced calculus |
| 250 | |a Si(metric) ed. | ||
| 264 | 1 | |a New York [u.a.] |b McGraw-Hill |c 1974 | |
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Record in the Search Index
| _version_ | 1804118672972709889 |
|---|---|
| adam_text | CONTENTS
Page
Chapter 1 NUMBERS 1
Sets. Real numbers. Decimal representation of real numbers. Geometric
representation of real numbers. Operations with real numbers. Inequali¬
ties. Absolute value of real numbers. Exponents and roots. Logarithms.
Axiomatic foundations of the real number system. Point sets. Intervals.
Countability. Neighbourhoods. Limit points. Bounds. Weierstrass Bolzano
theorem. Algebraic and transcendental numbers. The complex number
system. Polar form of complex numbers. Mathematical induction.
Chapter 2 FUNCTIONS, LIMITS AND CONTINUITY 20
Functions. Graph of a function. Bounded functions. Monotonic func¬
tions. Inverse functions. Principal values. Maxima and minima. Types
of functions. Special transcendental functions. Limits of functions.
Right and left hand limits. Theorems on limits. Infinity. Special limits.
Continuity. Right and left hand continuity. Continuity in an interval.
Theorems on continuity. Sectional continuity. Uniform continuity.
Chapter 3 SEQUENCES 41
Definition of a sequence. Limit of a sequence. Theorems on limits of
sequences. Infinity. Bounded, monotonic sequences. Least upper bound
and greatest lower bound of a sequence. Limit superior. Limit inferior.
Nested intervals. Cauchy s convergence criterion. Infinite series.
Chapter 4 DERIVATIVES 57
Definition of a derivative. Right and left hand derivatives. Differen¬
tiability in an interval. Sectional differentiability. Graphical inter¬
pretation of the derivative. Differentials. Rules for differentiation.
Derivatives of special functions. Higher order derivatives. Mean value
theorems. Rolle s theorem. The theorem of the mean. Cauchy s gen¬
eralized theorem of the mean. Taylor s theorem of the mean. Special
expansions. L Hospital s rules. Applications.
Chapter 5 INTEGRALS 80
Definition of a definite integral. Measure zero. Properties of definite
integrals. Mean value theorems for integrals. Indefinite integrals.
Fundamental theorem of integral calculus. Definite integrals with
variable limits of integration. Change of variable of integration.
Integrals of special functions. Special methods of integration. Improper
integrals. Numerical methods for evaluating definite integrals. Ap¬
plications.
Page
Chapter 6 PARTIAL DERIVATIVES 101
Functions of two or more variables. Dependent and independent
variables. Domain of a function. Three dimensional rectangular coordi¬
nate systems. Neighborhoods. Regions. Limits. Iterated limits. Con¬
tinuity. Uniform continuity. Partial derivatives. Higher order partial
derivatives. Differentials. Theorems on differentials. Differentiation
of composite functions. Euler s theorem on homogeneous functions.
Implicit functions. Jacobians. Partial derivatives using Jacobians.
Theorems on Jacobians. Transformations. Curvilinear coordinates.
Mean value theorems.
Chapter 7 VECTORS 134
Vectors and scalars. Vector algebra. Laws of vector algebra. Unit
vectors. Rectangular unit vectors. Components of a vector. Dot or
scalar product. Cross or vector product. Triple products. Axiomatic
approach to vector analysis. Vector functions. Limits, continuity and
derivatives of vector functions. Geometric interpretation of a vector
derivative. Gradient, divergence and curl. Formulas involving V.
Vector interpretation of Jacobians. Orthogonal curvilinear coordinates.
Gradient, divergence, curl and Laplacian in orthogonal curvilinear co¬
ordinates. Special curvilinear coordinates.
Chapter 8 APPLICATIONS OF PARTIAL DERIVATIVES 161
Applications to geometry. Tangent plane to a surface. Normal line to
a surface. Tangent line to a curve. Normal plane to a curve. Envelopes.
Directional derivatives. Differentiation under the integral sign. Maxima
and minima. Method of Lagrange multipliers for maxima and minima.
Applications to errors.
Chapter 9 MULTIPLE INTEGRALS 180
Double integrals. Iterated integrals. Triple integrals. Transformations
of multiple integrals.
Chapter 10 LINE INTEGRALS, SURFACE INTEGRALS AND
INTEGRAL THEOREMS 195
Line integrals. Vector notation for line integrals. Evaluation of line
integrals. Properties of line integrals. Simple closed curves. Simply
and multiply connected regions. Green s theorem in the plane. Condi¬
tions for a line integral to be independent of the path. Surface integrals.
The divergence theorem. Stokes theorem.
Chapter 11 INFINITE SERIES 224
Convergence and divergence of infinite series. Fundamental facts con¬
cerning infinite series. Special series. Geometric series. The p series.
Tests for convergence and divergence of series of constants. Comparison
test. Quotient test. Integral test. Alternating series test. Absolute
and conditional convergence. Ratio test. The nth root test. Raabe s
test. Gauss test. Theorems on absolutely convergent series. Infinite
sequences and series of functions. Uniform convergence. Special tests
for uniform convergence of series. Weierstrass M test. Dirichlet s test.
Theorems on uniformly convergent series. Power series. Theorems on
Page
power series. Operations with power series. Expansion of functions
in power series. Some important power series. Special topics. Func¬
tions denned by series. Bessel and hypergeometric functions. Infinite
series of complex terms. Infinite series of functions of two (or more)
variables. Double series. Infinite products. Summability. Asymptotic
series.
Chapter 12 IMPROPER INTEGRALS 260
Definition of an improper integral. Improper integrals of the first kind.
Special improper integrals of the first kind. Geometric or exponential
integral. The p integral of the first kind. Convergence tests for im¬
proper integrals of the first kind. Comparison test. Quotient test.
Series test. Absolute and conditional convergence. Improper integrals
of the second kind. Cauchy principal value. Special improper integrals
of the second kind. Convergence tests for improper integrals of the
second kind. Improper integrals of the third kind. Improper integrals
containing a parameter. Uniform convergence. Special tests for uniform
convergence of integrals. Weierstrass M test. Dirichlet s test. Theorems
on uniformly convergent integrals. Evaluation of definite integrals.
Laplace transforms. Improper multiple integrals.
Chapter 13 GAMMA AND BETA FUNCTIONS 285
Gamma function. Table of values and graph of the gamma function.
Asymptotic formula for V(n). Miscellaneous results involving the gamma
function. Beta function. Dirichlet integrals.
Chapter 14 FOURIER SERIES 298
Periodic functions. Fourier series. Dirichlet conditions. Odd and even
functions. Half range Fourier sine or cosine series. Parseval s identity.
Differentiation and integration of Fourier series. Complex notation for
Fourier series. Boundary value problems. Orthogonal functions.
Chapter 15 FOURIER INTEGRALS 321
The Fourier integral. Equivalent forms of Fourier s integral theorem.
Fourier transforms. Parseval s identities for Fourier integrals. The
convolution theorem.
Chapter 16 ELLIPTIC INTEGRALS 331
The incomplete elliptic integral of the first kind. The incomplete elliptic
integral of the second kind. The incomplete elliptic integral of the third
kind. Jacobi s forms for the elliptic integrals. Integrals reducible to
elliptic type. Jacobi s elliptic functions. Landen s transformation.
Chapter 17 FUNCTIONS OF A COMPLEX VARIABLE 345
Functions. Limits and continuity. Derivatives. Cauchy Riemann equa¬
tions. Integrals. Cauchy s theorem. Cauchy s integral formulas. Tay¬
lor s series. Singular points. Poles. Laurent s series. Residues. Residue
theorem. Evaluation of definite integrals.
INDEX 373
|
| any_adam_object | 1 |
| author | Spiegel, Murray R. 1923-1991 |
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| author_facet | Spiegel, Murray R. 1923-1991 |
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| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Si(metric) ed. |
| format | Book |
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| spelling | Spiegel, Murray R. 1923-1991 Verfasser (DE-588)109314840 aut Schaum's outline of theory and problems of advanced calculus by Murray R. Spiegel Theory and problems of advanced calculus Si(metric) ed. New York [u.a.] McGraw-Hill 1974 384 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Schaum's outline series Analyse (wiskunde) gtt Calcul - Problèmes et exercices ram Calculus Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Analysis (DE-588)4001865-9 s DE-604 Infinitesimalrechnung (DE-588)4072798-1 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002794088&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Spiegel, Murray R. 1923-1991 Schaum's outline of theory and problems of advanced calculus Analyse (wiskunde) gtt Calcul - Problèmes et exercices ram Calculus Infinitesimalrechnung (DE-588)4072798-1 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4072798-1 (DE-588)4001865-9 (DE-588)4143389-0 |
| title | Schaum's outline of theory and problems of advanced calculus |
| title_alt | Theory and problems of advanced calculus |
| title_auth | Schaum's outline of theory and problems of advanced calculus |
| title_exact_search | Schaum's outline of theory and problems of advanced calculus |
| title_full | Schaum's outline of theory and problems of advanced calculus by Murray R. Spiegel |
| title_fullStr | Schaum's outline of theory and problems of advanced calculus by Murray R. Spiegel |
| title_full_unstemmed | Schaum's outline of theory and problems of advanced calculus by Murray R. Spiegel |
| title_short | Schaum's outline of theory and problems of advanced calculus |
| title_sort | schaum s outline of theory and problems of advanced calculus |
| topic | Analyse (wiskunde) gtt Calcul - Problèmes et exercices ram Calculus Infinitesimalrechnung (DE-588)4072798-1 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Analyse (wiskunde) Calcul - Problèmes et exercices Calculus Infinitesimalrechnung Analysis Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002794088&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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