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999 _c93967
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008 250115s2024 njua b 001 0 eng
010 _a 2023009931
020 _a9789811273896
_q(paperback)
020 _a9789811272981
_q(hardcover)
020 _z9789811272998
_q(ebook for institutions)
020 _z9789811273001
_q(ebook for individuals)
035 _a23051571
040 _aDLC
_beng
_erda
_cDLC
_dDLC
041 _aeng
042 _apcc
050 0 0 _aQA305
_b.J86 2024
082 0 0 _a515/.33
_223/eng20230711
100 1 _aJungić, Veselin,
_eauthor.
245 1 0 _aDifferential calculus :
_bproblems and solutions from fundamentals to nuances /
_cVeselin Jungić, Petra Menz, Randall Pyke.
264 1 _aNew Jersey :
_bWorld Scientific,
_c[2024]
300 _axxxiii, 293 pages :
_billustrations ;
_c24 cm
336 _atext
_btxt
_2rdacontent
337 _aunmediated
_bn
_2rdamedia
338 _avolume
_bnc
_2rdacarrier
504 _aIncludes bibliographical references (page 287) and index.
505 0 _8Contents Preliminaries 1 Symbols 2 Commonly Used Mathematical Facts 2.1 Identities 2.2 Plane figures 2.3 Solids 3 Functions 3.1 Definitions 3.2 Bank of functions 3.3 Graphs of commonly used functions 1. Limits and Continuity 1.1 Introduction 1.2 Types of Limits 1.2.1 Routine miscellaneous limits 1.2.2 Not-so-routine miscellaneous limits 1.2.3 Left-hand and right-hand limits 1.2.4 Limit at infinity 1.2.5 Trigonometric limits 1.2.6 Limit definition of the number e 1.2.7 Squeeze Theorem 1.2.8 L’Hospital’s Rule 1.2.9 Indeterminate forms of types 00, ∞0, and 1∞ 1.2.10 Asymptotes 1.2.11 ε–δ limit definition 1.3 Continuity 1.3.1 Intermediate Value Theorem 1.4 Answers, Hints, and Solutions 2. Derivatives 2.1 Introduction 2.2 Definition of Derivative and Differentiation Rules 2.2.1 Definition of derivative 2.2.2 Continuity and differentiation 2.2.3 Differentiation rules 2.2.4 Higher-order derivatives 2.2.5 Not-so-routine differentiation 2.3 Implicit and Logarithmic Differentiation 2.3.1 Implicit differentiation 2.3.2 Logarithmic differentiation 2.4 Tangent Lines 2.4.1 Tangent lines to explicitly defined functions 2.4.2 Tangent lines to implicitly defined functions 2.4.3 Not-so-routine tangent line problems 2.5 Related Rates 2.5.1 Pythagorean relationship 2.5.2 Trigonometric relationship 2.5.3 Similar triangles 2.5.4 Area and volume 2.5.5 Miscellaneous relationships 2.6 Answers, Hints, and Solutions 3. Functions and Their Graphs 3.1 Introduction 3.2 Properties of Functions and Their Graphs 3.2.1 Routine questions 3.2.2 Not-so-routine questions 3.3 Sketching Graphs of Functions 3.4 Answers, Hints, and Solutions 4. Optimization 4.1 Introduction 4.2 Routine Questions 4.3 Not-So-Routine Questions 4.4 Answers, Hints, and Solutions 5. Other Applications of Differentiation 5.1 Introduction 5.2 Rolle’s Theorem and the Mean Value Theorem 5.3 Approximation 5.3.1 Differential 5.3.2 Method of linear approximation 5.3.3 Newton’s method of approximation 5.3.3.1 Routine questions 5.3.3.2 Not-so-routine questions 5.4 Antiderivatives and Initial Value Problems 5.5 Natural Growth and Decay 5.5.1 Routine questions 5.5.2 Not-so-routine questions 5.6 Answers, Hints, and Solutions 6. Parametric and Polar Curves 6.1 Introduction 6.2 Parametric Curves 6.2.1 Routine problems 6.2.2 Not-so-routine problems 6.3 Polar Curves 6.3.1 Routine problems 6.3.2 Not-so-routine problems 6.4 Answers, Hints, Solutions 7. True–False and Multiple Choice Questions 7.1 Functions 7.1.1 True or false 7.1.2 Multiple choice questions 7.2 Limits 7.2.1 True or false 7.2.2 Multiple choice questions 7.3 Continuity 7.3.1 True or false 7.3.2 Multiple choice questions 7.4 Derivatives 7.4.1 True or false 7.4.2 Multiple choice questions 7.5 Applications of Derivatives 7.5.1 True or false 7.5.2 Multiple choice questions 7.6 Antiderivatives 7.6.1 True or false 7.6.2 Multiple choice questions 7.7 Parametric Equations and Polar Coordinates 7.7.1 True or false 7.7.2 Multiple choice questions 7.8 Examples, Definitions, and Theorems 7.9 Answers, Hints, and Solutions 8. Recommendations to Thrive in Mathematics 8.1 Tips for Reading these Recommendations 8.2 Habits of a Thriving Student 8.3 How to Prepare for Exams 8.4 Getting and Staying Connected 8.5 Staying Healthy 8.6 Resources Bibliography Index
520 _a"This volume contains more than 900 problems in differential calculus, covering limits, continuity, derivatives, and their applications. The applications are comprised of a variety of approximations, growth and decay, optimization, curve sketching techniques, and analytical tools to investigate properties of parametrically given planar curves. The problems are sorted by topic, each opening with with a summary of the relevant mathematical notions and their properties. Through a careful selection of appropriate problems in each chapter, the book clearly communicates some of the big ideas and applications in calculus: the notion of a function, the notion of an infinitesimal, the notion of a differentiable function, and the notion of an approximation, among others. The book provides the answers to each problem, often with a detailed sketch of the solution process. With about 260 true-false and multiple-choice questions, the book provides its users with an accessible way to assess and practice their understanding of calculus related facts and nuances. More than 180 figures are included to help readers to visualize properties of functions, illustrate word problems, depict solutions, and provide an extensive bank of polar curves. The purpose of this problem collection is to serve as a supplementary learning resource for students who are studying university-level differential calculus. The book also acts as a teaching resource for calculus instructors"--
_cProvided by publisher.
650 0 _aDifferential calculus.
650 0 _aDifferential calculus
_vProblems, exercises, etc.
700 1 _aMenz, Petra,
_eauthor.
700 1 _aPyke, Randall,
_eauthor.
942 _2ddc
_cBK