Banner A. - Calculus Lifesaver (2007)

Pages :  753
type : PDF

contents :   Functions, Graphs, and Lines, Review of Trigonometry,  Introduction to Limits, How to Solve Limit Problems Involving Polynomials,  Continuity and Di�erentiability,  How to Solve Di�erentiation Problems,  Trig Limits and Derivatives,  Implicit Di�erentiation and Related Rates,  Exponentials and Logarithms,  De�nition of e,  Di�erentiation of Logs and Exponentials,  How to Solve Limit Problems Involving Exponentials or Logs,   Logarithmic Di�erentiation, Exponential Growth and Decay, Hyperbolic Functions,  Inverse Functions and Inverse Trig Functions,  The Derivative and Graphs, Sketching Graphs,  Optimization and Linearization,  L'H^opital's Rule and Overview of Limits,  Introduction to Integration,  De�nite Integrals,  The Fundamental Theorems of Calculus,  Techniques of Integration, Part One, Techniques of Integration, Part two,  Improper Integrals: Basic Concepts,  Improper Integrals: How to Solve Problems,  Sequences and Series: Basic Concepts,  How to Solve Series Problems,  Taylor Polynomials, Taylor Series, and Power Series,  How to Solve Estimation Problems,  Taylor and Power Series: How to Solve Problems,  Parametric Equations and Polar Coordinates,   Complex Numbers,  Volumes, Arc Lengths, and Surface Areas,  Di�erential Equations,  Appendix A Limits and Proofs,  Appendix B Estimating Integrals,  List of Symbols

Callahan J. et al - Calculus in Context (2008)

James Callahan
Kenneth Hoffman
David Cox
Donal O’Shea
Harriet Pollatsek
Lester Senechal

pages: 870
file type ; PDF

Main contents :  A Context for Calculus,  Successive Approximations, The Derivative, Diﬀerential Equations, Techniques of Diﬀerentiation, The Integral, Periodicity, Dynamical Systems, Functions of Several Variables, Series and Approximations, Techniques of Integration, Case Studies,

Chung S. K. - Universtanding basic calculus (2014)

File Type  :   PDF

pages : 292

Contents:
Exponents .  Algebraic Identities and Algebraic Expressions . Solving Linear Equations . Solving Quadratic Equations . Remainder Theorem and Factor Theorem . Solving Linear Inequalities . Lines .Pythagoras Theorem, Distance Formula and Circles . Parabola . Systems of Equations .

Sets, Real Numbers and Inequalities, Functions and Graphs,  Limits,  Di�erentiation,  Applications of Di�erentiation , Integration , Trigonometric Functions , Exponential and Logarithmic Functions ,More Di�erentiation .More Integration

Clark W. D. & McCune S. L. - Practice Makes Perfect Calculus (2010)

Pages :  160

Type  :   PDF

Contents  :

I LIMITS 1
1 The limit concept  3
Limit deﬁnition and intuition  3
Properties of limits  4
2 Special limits 7
Zero denominator limits 7
Inﬁnite limits and limits involving inﬁnity 8
Left-hand and right-hand limits 9
3 Continuity  11
Deﬁnition of continuity  11
Properties of continuity  12
Intermediate Value Theorem (IVT)  13
II DIFFERENTIATION 15
4   Deﬁnition of the derivative and derivatives
of some simple functions  17
Deﬁnition of the derivative  17
Derivative of a constant function  18
Derivative of a linear function  19
Derivative of a power function  19
Numerical derivatives  20
5 Rules of differentiation  23
Constant multiple of a function rule  23
Rule for sums and differences  24
Product rule  25
Quotient rule  26
Chain rule  28
Implicit differentiation  29
Derivative of the natural exponential function ex 33
Derivative of the natural logarithmic function lnx 34
Derivatives of exponential functions for bases other than e 34
Derivatives of logarithmic functions for bases other than e 35
Derivatives of trigonometric functions  36
Derivatives of inverse trigonometric functions  37
Higher-order derivatives  39
III INTEGRATION 41
7 Indeﬁnite integral and basic integration
formulas and rules  43
Antiderivatives and the indeﬁnite integral  43
Integration of constant functions  44
Integration of power functions  45
Integration of exponential functions  46
Integration of derivatives of trigonometric functions  47
Integration of derivatives of inverse trigonometric functions 48
Two useful integration rules  49
8 Basic integration techniques 53
Integration by substitution 53
Integration by parts  55
Integration by using tables of integral formulas  57
9 The deﬁnite integral 61
Deﬁnition of the deﬁnite integral and the
First Fundamental Theorem of Calculus 61
Useful properties of the deﬁnite integral 62
Second Fundamental Theorem of Calculus 64
Mean Value Theorem for Integrals 65
IV APPLICATIONS OF THE DERIVATIVE
AND THE DEFINITE INTEGRAL 67
10 Applications of the derivative  69
Slope of the tangent line at a point  69
Instantaneous rate of change 70
Differentiability and continuity 72
Increasing and decreasing functions, extrema, and critical points 73
Concavity and points of inﬂection 77
Mean Value Theorem  79
11 Applications of the deﬁnite integral 83
Area of a region under one curve 83
Area of a region between two curves 84
Length of an arc 86
Appendix A: Basic functions and their graphs  89
Appendix B: Basic differentiation formulas and rules 97
Appendix C: Integral formulas 99
Worked solutions  117

Cohen D. et al - Precalculus (2012)

file type :  pdf

pages  :  1186

Contents
Fundamentals 1
1.1 Sets of Real Numbers 1
1.2 Absolute Value 6
1.3 Solving Equations (Review and Preview) 10
1.4 Rectangular Coordinates. Visualizing Data 19
1.5 Graphs and Graphing Utilities 31
1.6 Equations of Lines 42
1.7 Symmetry and Graphs. Circles 56
Equations and Inequalities 81
2.1 Quadratic Equations: Theory and Examples 81
2.2 Other Types of Equations 92
2.3 Inequalities 103
2.4 More on Inequalities 112
Functions 127
3.1 The Deﬁnition of a Function 127
3.2 The Graph of a Function 141
3.3 Shapes of Graphs. Average Rate of Change 154
3.4 Techniques in Graphing 166
3.5 Methods of Combining Functions. Iteration 181
3.6 Inverse Functions 194
Polynomial and Rational Functions.
Applications to Optimization 215
4.1 Linear Functions 215
4.3 Using Iteration to Model Population Growth
(Optional Section, Online) 247
4.4 Setting Up Equations That Deﬁne Functions 248
4.5 Maximum and Minimum Problems 259
4.6 Polynomial Functions 274
4.7 Rational Functions 296
Exponential and Logarithmic Functions 323
5.1 Exponential Functions 325
5.2 The Exponential Function y � ex
5.3 Logarithmic Functions 346
5.4 Properties of Logarithms 361
5.5 Equations and Inequalities with Logs and Exponents 371
5.6 Compound Interest 382
5.7 Exponential Growth and Decay 392
An Introduction to Trigonometry
via Right Triangles 420
6.1 Trigonometric Functions of Acute Angles 420
6.2 Right-Triangle Applications 435
6.3 Trigonometric Functions of Angles 441
6.4 Trigonometric Identities 454
The Trigonometric Functions 467
7.2 Trigonometric Functions of Angles 481
7.3 Evaluating the Trigonometric Functions 492
7.4 Algebra and the Trigonometric Functions 501
7.5 Right-Triangle Trigonometry 511
Graphs of the Trigonometric Functions 530
8.1 Trigonometric Functions of Real Numbers 531
8.2 Graphs of the Sine and Cosine Functions 543
8.3 Graphs of y � A sin(Bx � C) and y � A cos(Bx � C) 560
8.4 Simple Harmonic Motion 576
8.5 Graphs of the Tangent and the Reciprocal Functions 583
Analytical Trigonometry 599
9.2 The Double-Angle Formulas 611
9.3 The Product-to-Sum and Sum-to-Product Formulas 620
9.4 Trigonometric Equations 628
9.5 The Inverse Trigonometric Functions 642
10.1 Right-Triangle Applications 663
10.2 The Law of Sines and the Law of Cosines 681
10.3 Vectors in the Plane: A Geometric Approach 697
10.4 Vectors in the Plane: An Algebraic Approach 706
10.5 Parametric Equations 714
10.6 Introduction to Polar Coordinates 722
10.7 Curves in Polar Coordinates 732
10.8 Demoivre’s Theorem 740
Systems of Equations 757
11.1 Systems of Two Linear Equations in Two Unknowns 757
11.2 Gaussian Elimination 769
11.3 Matrices 782
11.4 The Inverse of a Square Matrix 795
11.5 Determinants and Cramer’s Rule 809
11.6 Nonlinear Systems of Equations 822
11.7 Systems of Inequalities 829
The Conic Sections 841
12.1 The Basic Equations 841
12.2 The Parabola 850
12.3 Tangents to Parabolas (Optional Section) 862
12.4 The Ellipse 864
12.5 The Hyperbola 879
12.6 The Focus–Directrix Property of Conics 889
12.7 The Conics in Polar Coordinates 898
12.8 Rotation of Axes 903
Roots of Polynomial Equations 919
13.1 Division of Polynomials 920
13.2 The Remainder Theorem and the Factor Theorem 926
13.3 The Fundamental Theorem of Algebra 935
13.4 Rational and Irrational Roots 945
13.5 Conjugate Roots and Descartes’ Rule of Signs 954
13.6 Introduction to Partial Fractions 960
13.7 More About Partial Fractions 967
14.1 Mathematical Induction 983
14.2 The Binomial Theorem 989
14.3 Introduction to Sequences and Series 999
14.4 Arithmetic Sequences and Series 1009
14.5 Geometric Sequences and Series 1014
14.6 An Introduction to Limits 1019
Appendix A A-1
A.1 Signiﬁcant Digits A-1
A.2 Is Irrational A-4
A.3 The Complex Number System A-5
Appendix B (online)* B-1
B.1 Review of Integer Exponents B-1
B.2 Review of nth Roots B-7
B.3 Review of Rational Exponents B-14
B.4 Review of Factoring B-18
B.5 Review of Fractional Expressions B-23
B.6 Properties of the Real Numbers B-28