College Algebra and Calculus: An Applied Approach

Applications......Page 3
Contents......Page 8
Preface......Page 14
Instructor Resources......Page 17
Student Resources......Page 18
Acknowledgements......Page 19
Ch 0: Fundamental Concepts of Algebra......Page 22
0.1 Real Numbers: Order and Absolute Value......Page 23
0.2 The Basic Rules of Algebra......Page 31
0.3 Integer Exponents......Page 41
0.4 Radicals and Rational Exponents......Page 50
0.5 Polynomials and Special Products......Page 61
0.6 Factoring......Page 69
0.7 Fractional Expressions......Page 76
Algebra Tutor......Page 83
Summary and Study Strategies......Page 85
Review Exercises......Page 87
Test Yourself......Page 89
Ch 1: Equations and Inequalities......Page 90
1.1 Linear Equations......Page 91
1.2 Mathematical Modeling......Page 101
1.3 Quadratic Equations......Page 114
1.4 The Quadratic Formula......Page 125
1.5 Other Types of Equations......Page 136
1.6 Linear Inequalities......Page 147
1.7 Other Types of Inequalities......Page 159
Algebra Tutor......Page 169
Summary and Study Strategies......Page 171
Review Exercises......Page 173
Test Yourself......Page 177
Ch 2: Functions and Graphs......Page 178
2.1 Graphs of Equations......Page 179
2.2 Lines in the Plane......Page 193
2.3 Linear Modeling and Direct Variation......Page 204
2.4 Functions......Page 216
2.5 Graphs of Functions......Page 230
2.6 Transformations of Functions......Page 241
2.7 The Algebra of Functions......Page 251
Algebra Tutor......Page 261
Summary and Study Strategies......Page 263
Review Exercises......Page 265
Test Yourself......Page 269
Ch 3: Polynomial and Rational Functions......Page 270
3.1 Quadratic Functions and Models......Page 271
3.2 Polynomial Functions of Higher Degree......Page 283
3.3 Polynomial Division......Page 293
3.4 Real Zeros of Polynomial Functions......Page 303
3.5 Complex Numbers......Page 318
3.6 The Fundamental Theorem of Algebra......Page 327
3.7 Rational Functions......Page 335
Algebra Tutor......Page 347
Summary and Study Strategies......Page 349
Review Exercises......Page 351
Test Yourself......Page 355
Ch 4: Exponential and Logarithmic Functions......Page 356
4.1 Inverse Functions......Page 357
4.2 Exponential Functions......Page 367
4.3 Logarithmic Functions......Page 379
4.4 Properties of Logarithms......Page 390
4.5 Solving Exponential and Logarithmic Equations......Page 398
4.6 Exponential and Logarithmic Models......Page 408
Algebra Tutor......Page 421
Summary and Study Strategies......Page 423
Review Exercises......Page 425
Test Yourself......Page 429
Ch 5: Systems of Equations and Inequalities......Page 430
5.1 Solving Systems Using Substitution......Page 431
5.2 Solving Systems Using Elimination......Page 441
5.3 Linear Systems in Three or More Variables......Page 453
5.4 Systems of Inequalities......Page 466
5.5 Linear Programming......Page 475
Summary and Study Strategies......Page 487
Algebra Tutor......Page 485
Review Exercises......Page 488
Test Yourself......Page 493
Ch 6: Matrices and Determinants......Page 494
6.1 Matrices and Linear Systems......Page 495
6.2 Operations with Matrices......Page 508
6.3 The Inverse of a Square Matrix......Page 523
6.4 The Determinant of a Square Matrix......Page 534
6.5 Applications of Matrices and Determinants......Page 542
Algebra Tutor......Page 551
Summary and Study Strategies......Page 553
Review Exercises......Page 555
Test Yourself......Page 559
Ch 7: Limits and Derivatives......Page 560
7.1 Limits......Page 561
7.2 Continuity......Page 574
7.3 The Derivative and the Slope of a Graph......Page 584
7.4 Some Rules for Differentiation......Page 595
7.5 Rates of Change: Velocity and Marginals......Page 608
7.6 The Product and Quotient Rules......Page 622
7.7 The Chain Rule......Page 632
Algebra Tutor......Page 641
Summary and Study Strategies......Page 643
Review Exercises......Page 645
Test Yourself......Page 649
Ch 8: Applications of the Derivative......Page 650
8.1 Higher-Order Derivatives......Page 651
8.2 Implicit Differentiation......Page 658
8.3 Related Rates......Page 665
8.4 Increasing and Decreasing Functions......Page 673
8.5 Extrema and the First-Derivative Test......Page 682
8.6 Concavity and the Second-Derivative Test......Page 691
Algebra Tutor......Page 701
Summary and Study Strategies......Page 703
Review Exercises......Page 705
Test Yourself......Page 709
Ch 9: Further Applications of the Derivative......Page 710
9.1 Optimization Problems......Page 711
9.2 Business and Economic Applications......Page 719
9.3 Asymptotes......Page 729
9.4 Curve-Sketching: A Summary......Page 741
9.5 Differentials and Marginal Analysis......Page 750
Algebra Tutor......Page 757
Summary and Study Strategies......Page 759
Review Exercises......Page 760
Test Yourself......Page 763
Ch 10: Derivatives of Exponential and Logarithmic Functions......Page 764
10.1 Exponential Functions......Page 765
10.2 Natural Exponential Functions......Page 771
10.3 Derivatives of Exponential Functions......Page 780
10.4 Logarithmic Functions......Page 789
10.5 Derivatives of Logarithmic Functions......Page 798
10.6 Exponential Growth and Decay......Page 807
Algebra Tutor......Page 815
Summary and Study Strategies......Page 817
Review Exercises......Page 819
Test Yourself......Page 823
Ch 11: Integration and Its Applications......Page 824
11.1 Antiderivatives and Indefinite Integrals......Page 825
11.2 Integration by Substitution and the General Power Rule......Page 835
11.3 Exponential and Logarithmic Integrals......Page 844
11.4 Area and the Fundamental Theorem of Calculus......Page 852
11.5 The Area of a Region Bounded by Two Graphs......Page 864
11.6 The Definite Integral as the Limit of a Sum......Page 873
Algebra Tutor......Page 879
Summary and Study Strategies......Page 881
Review Exercises......Page 883
Test Yourself......Page 887
Ch 12: Techniques of Integration......Page 888
12.1 Integration by Parts and Present Value......Page 889
12.2 Integration Tables......Page 899
12.3 Numerical Integration......Page 907
12.4 Improper Integrals......Page 916
Algebra Tutor......Page 925
Summary and Study Strategies......Page 927
Review Exercises......Page 929
Test Yourself......Page 931
Ch 13: Functions of Several Variables......Page 932
13.1 The Three-Dimensional Coordinate System......Page 933
13.2 Surfaces in Space......Page 940
13.3 Functions of Several Variables......Page 949
13.4 Partial Derivatives......Page 957
13.5 Extrema of Functions of Two Variables......Page 968
13.6 Lagrange Multipliers......Page 978
13.7 Least Squares Regression Analysis......Page 986
13.8 Double Integrals and Area in the Plane......Page 993
13.9 Applications of Double Integrals......Page 1001
Algebra Tutor......Page 1009
Summary and Study Strategies......Page 1011
Review Exercises......Page 1013
Test Yourself......Page 1017
Answers to Selected Exercises......Page 1018
Answers to Checkpoints......Page 1115
Answers to Tech Tutors......Page 1127
Index......Page 1128