

1  (26) 

Polynomials and Rational Functions 


1  (3) 

Graphing Calculators and Computer Algebra Systems 


4  (4) 


8  (4) 

Trigonometric and Inverse Trigonometric Functions 


12  (4) 

Exponential and Logarithmic Functions 


16  (4) 

Transformations of Functions 


20  (7) 


23  (4) 


27  (28) 

A Brief Preview of Calculus 


27  (2) 


29  (3) 


32  (3) 

Continuity and its Consequences 


35  (4) 

Limits Involving Infinity 


39  (4) 

Formal Definition of the Limit 


43  (5) 

Limits and LossofSignificance Errors 


48  (7) 


51  (4) 


55  (40) 

Tangent Lines and Velocity 


55  (5) 


60  (5) 

Computation of Derivatives: The Power Rule 


65  (4) 

The Product and Quotient Rules 


69  (4) 


73  (3) 

Derivatives of Trigonometric Functions 


76  (3) 

Derivatives of Exponential and Logarithmic Functions 


79  (3) 

Implicit Differentiation and Inverse Trig. Functions 


82  (5) 


87  (8) 


90  (5) 

Applications of Differentiation 


95  (56) 

Linear Approximations and Newton's Method 


95  (5) 

Indeterminate Forms and L'Hopital's Rule 


100  (3) 

Maximum and Minimum Values 


103  (6) 

Increasing and Decreasing Functions 


109  (7) 

Concavity and the Second Derivative Test 


116  (6) 

Overview of Curve Sketching 


122  (9) 


131  (7) 


138  (3) 

Rates of Change in Economics and the Sciences 


141  (10) 


144  (7) 


151  (36) 


151  (3) 


154  (3) 


157  (5) 


162  (5) 

The Fundamental Theorem Of Calculus 


167  (5) 

Integration by Substitution 


172  (5) 


177  (4) 

The Natural Logarithm As An Integral 


181  (6) 


183  (4) 

Applications of the Definite Integral 


187  (37) 


187  (5) 

Volume: Slicing, Disks and Washers 


192  (5) 

Volumes by Cylindrical Shells 


197  (4) 

Arc Length and Surface Area 


201  (4) 


205  (7) 

Applications of Integration to Physics and Engineering 


212  (4) 


216  (8) 


220  (4) 


224  (27) 

Review of Formulas and Techniques 


224  (1) 


225  (6) 

Trigonometric Techniques of Integration 


231  (3) 

Integration of Rational Functions Using Partial Fractions 


234  (4) 

Integration Table and Computer Algebra Systems 


238  (2) 


240  (11) 


246  (5) 

FirstOrder Differential Equations 


251  (26) 

Modeling with Differential Equations 


251  (4) 

Separable Differential Equations 


255  (9) 

Direction Fields and Euler's Method 


264  (4) 

Systems of FirstOrder Differential Equations 


268  (9) 


272  (5) 


277  (46) 

Sequences of Real Numbers 


277  (3) 


280  (4) 

The Integral Test and Comparison Tests 


284  (5) 


289  (3) 

Absolute Convergence and the Ratio Test 


292  (3) 


295  (6) 


301  (7) 

Applications of Taylor Series 


308  (3) 


311  (12) 


318  (5) 

Parametric Equations and Polar Coordinates 


323  (34) 

Plane Curves and Parametric Equations 


323  (5) 

Calculus and Parametric Equations 


328  (6) 

Arc Length and Surface Area in Parametric Equations 


334  (2) 


336  (6) 

Calculus and Polar Coordinates 


342  (4) 


346  (3) 

Conic Sections in Polar Coordinates 


349  (8) 


352  (5) 

Vectors and the Geometry of Space 


357  (18) 


357  (2) 


359  (2) 


361  (3) 


364  (2) 

Lines and Planes in Space 


366  (2) 


368  (7) 


372  (3) 


375  (19) 


375  (4) 

The Calculus of VectorValued Functions 


379  (1) 


380  (3) 


383  (3) 

Tangent and Normal Vectors 


386  (3) 


389  (5) 


391  (3) 

Functions of Several Vars. and Partial Diff. 


394  (33) 

Functions of Several Variables 


394  (3) 


397  (3) 


400  (2) 

Tangent Planes and Linear Approximations 


402  (4) 


406  (2) 

The Gradient and Directional Derivatives 


408  (3) 

Extrema of Functions of Several Variables 


411  (6) 

Constrained Optimization and Lagrange Multipliers 


417  (10) 


422  (5) 


427  (54) 


427  (8) 

Area, Volume and Center of Mass 


435  (10) 

Double Integrals In Polar Coordinates 


445  (6) 


451  (4) 


455  (7) 


462  (4) 


466  (7) 

Change of Variables in Multiple Integrals 


473  (8) 


475  (6) 


481  (52) 


481  (4) 


485  (6) 

Independence of Path and Conservative Vector Fields 


491  (5) 


496  (4) 


500  (7) 


507  (8) 


515  (4) 


519  (4) 

Applications of Vector Calculus 


523  (10) 


526  (7) 

Second Order Differential Equations 


533  (20) 

SecondOrder Equations with Constant Coefficients 


533  (4) 

Nonhomogeneous Equations: Undetermined Coefficients 


537  (5) 

Applications of Second Order Equations 


542  (6) 

Power Series Solutions of Differential Equations 


548  (5) 


553  