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Collection of Problems on a Course of Mathematical Analysis contains selected problems and exercises on the main branches of a Technical College course of mathematical analysis. This book covers the topics of functions, limits, derivatives, differential calculus, curves, definite integral, integral calculus, methods of evaluating definite integrals, and their applications.
Other topics explored include numerical problems related to series and the functions of several variables in differential calculus, as well as their applications. The remaining chapters examine the principles of multiple, line, and surface integrals, the trigonometric series, and the elements of the theory of fields.
This book is intended for students studying mathematical analysis within the framework of a technical college course. We are always looking for ways to improve customer experience on Elsevier. We would like to ask you for a moment of your time to fill in a short questionnaire, at the end of your visit.
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Published Date: 1st January Page Count: Flexible - Read on multiple operating systems and devices. Easily read eBooks on smart phones, computers, or any eBook readers, including Kindle. Institutional Subscription. Free Shipping Free global shipping No minimum order. Foreword to the Tenth Russian Edition I.
Functions 1. Functions and Methods of Specifying Them 2. Notation for and Classification of Functions 3. Elementary Investigation of Functions 4. Elementary Functions 5. The Inverse Functions. Power, Exponential and Logarithmic Functions 6.
The Trigonometric and Inverse Trigonometric Functions 7. Numerical Problems II. Limits 1. Basic Definitions 2. Orders of Magnitude. Tests for the Existence of a Limit 3. Continuous Functions 4. Finding Limits. Comparison of Infinitesimals III. Derivatives and Differentials. Differential Calculus 1. The Rate of Change of a Function 2. Differentiation of Functions 3. Differentiability of a Function 4. Derivative as Rate of Change Further Examples 5.
Repeated Differentiation IV. The Investigation of Functions and Curves 1. The Behaviour of a Function "at a Point" 2.
Applications of the First Derivative 3. Applications of the Second Derivative 4. Auxiliary Problems. Solution of Equations 5.
Taylor's Formula and its Applications 6. Curvature 7. Numerical Problems V. The Definite Integral 1. The Definite Integral and its Elementary Properties 2. The Indefinite Integral. Integral Calculus 1. Elementary Examples of Integration 2. Basic Methods of Integration 3. Methods of Evaluating Definite Integrals. Improper Integrals 1. Methods of Exact Evaluation of Integrals 2. Approximation Methods 3. Applications of the Integral 1. Some Problems of Geometry and Statics 2.
Some Problems of Physics IX. Series 1. Numerical Series 2. Functional Series 3. Power Series 4. Some Applications of Taylor's Series 5.
Numerical Problems X. Functions of Several Variables. Functions of Several Variables 2. Elementary Investigation of a Function 3. Derivatives and Differentials of Functions of Several Variables 4. Differentiation of Functions 5. Repeated Differentiation XI.
Taylor's Formula. Extrema of Functions of Several Variables 2. Plane Curves 3. Vector Functions of a Scalar Argument. Curves in Space. Surfaces 4. Scalar Field. Directional Derivative XII. Multiple Integrals and Iterated Integration 1. Double and Triple Integrals 2. Iterated Integration 3. Integrals in Polar, Cylindrical and Spherical Coordinates 4.
Applications of Double and Triple Integrals 5. Improper Integrals. Line and Surface Integrals 1. Line Integrals 2.
A Problem Book in Mathematical Analysis
A Collection of Problems on a Course of Mathematical Analysis