tailieunhanh - Department of Mathematical Sciences

The notes contain the material that I use when preparing lectures for a course I gave from the mid 1980's until 1994; in that sense they are my lecture notes. "Lectures were once useful, but now when all can read, and books are so nu- merous, lectures are unnecessary." Samuel Johnson, 1799. Lecture notes have been around for centuries, either informally, as handwritten notes, or formally as textbooks. Recently improvements in typesetting have made it easier to produce \personalised" printed notes as here, but there has been no fundamental change. Experience shows that very few people are able to use lecture notes as a substitute for lectures; if. | Department of Mathematical Sciences Advanced Calculus and Analysis MA1002 Ian Craw ii April 13 2000 Version Copyright 2000 by Ian Craw and the University of Aberdeen All rights reserved. Additional copies may be obtained from Department of Mathematical Sciences University of Aberdeen Aberdeen AB9 2TY DSN mth200-101982-8 Foreword These Notes The notes contain the material that I use when preparing lectures for a course I gave from the mid 1980 s until 1994 in that sense they are my lecture notes. Lectures were once useful but now when all can read and books are so numerous lectures are unnecessary. Samuel Johnson 1799. Lecture notes have been around for centuries either informally as handwritten notes or formally as textbooks. Recently improvements in typesetting have made it easier to produce personalised printed notes as here but there has been no fundamental change. Experience shows that very few people are able to use lecture notes as a substitute for lectures if it were otherwise lecturing as a profession would have died out by now. These notes have a long history a first course in analysis rather like this has been given within the Mathematics Department for at least 30 years. During that time many people have taught the course and all have left their mark on it clarifying points that have proved difficult selecting the right examples and so on. I certainly benefited from the notes that Dr Stuart Dagger had written when I took over the course from him and this version builds on that foundation itslef heavily influenced by Spivak 1967 which was the recommended textbook for most of the time these notes were used. The notes are written in JATEX which allows a higher level view of the text and simplifies the preparation of such things as the index on page 101 and numbered equations. You will find that most equations are not numbered or are numbered symbolically. However sometimes I want to refer back to an equation and in that case it is numbered within the .

• Thư viện thông tin
• Good Foundations
• Sequences
• Monotone Convergence
• Dierentiability
• Innite Series
• Power Series
• Functions
• Several Variables
• Fixed point
• Linear equations in several variables
• Quasi normed space
• Several variables in quasi normed spaces
• Generalized linear equations
• Analytic functions
• Linear k positive operators
• Korovkin type theorems
• Complex variables
• Uniqueness problem
• Meromorphic functions
• Difference operators
• Several complex variables
• The plane integral
• space integral
• line integral
• surface integral
• Semi polar coordinates
• Gradient
• Directional derivative
• Partial derivatives
• The chain rule
• higher order
• Tangents to curves
• Tangent plane to a surface
• Simple integrals
• Extremum
• Extrema
• Rule of Four
• Functions and change
• Exponential functions
• Functions os several variables
• A fundamental tool
• Differentiating functions of several variables
• báo cáo của tạp chí Journal of Operator Theory
• tài liệu báo cáo nghiện cứu khoa học
• cách trình bày báo cáo
• kiến thức toán học
• báo cáo toán học
• trigonometric polynomials
• Calculation
• Approximating polynomials
• Gradient fields
• Rectangular coordinates
• Polar coordinates
• Maximum and minimum
• Spherical coordinates
• Point Sets
• Examinations of functions
• Level curves
• level surfaces
• Conics
• Continuous functions
• Description of curves
• Connected sets
• Space integrals
• Volume
• Moment of inertia
• centre of gravity
• Improper space integrals
• Line integrals
• Arc lengths
• parametric descriptions
• Tangential line integrals
• Gradient elds
• integrals
• vector eld
• divergence
• rotation
• Gauβ’s theorem
• Stokes’s theorem
• Nabla calculus
• Vector potentials
• Green’s identities
• Curvilinear coordinates
• m Electromagnetism
• Miscellaneous
• chain rule
• plane integral
• antiderivatives
• tài liệu báo cáo nghiên cứu khoa học
• công trình toán học
• báo cáo hóa học
• công trình nghiên cứu về hóa học
• tài liệu về hóa học
• Functions of Several variables
• Toán ứng dụng
• Toán cao cấp
• Calculus and its applications
• Công thức toán học
• Đại số giới hạn
• Fundamentals of calculus
• Integral calculus
• Techniques of integration
• Series and summations
• Applications to probability
• Marginal functions
• Comparative statics
• Partial elasticity
• Natural logarithm functions
• Economic functions
• Olive oil market volatility
• GARCH techniques
• ARCH techniques
• Several explanatory variables
• Business decisions