Calculus

Este livro foi feito por Gilbert Strang

Aqui em baixo estão os capítulos .

1: Introduction to Calculus, pp. 1-43

1.1 Velocity and Distance, pp. 1-7
1.2 Calculus Without Limits, pp. 8-15
1.3 The Velocity at an Instant, pp. 16-21
1.4 Circular Motion, pp. 22-28
1.5 A Review of Trigonometry, pp. 29-33
1.6 A Thousand Points of Light, pp. 34-35
1.7 Computing in Calculus, pp. 36-43

2: Derivatives, pp. 44-90

2.1 The Derivative of a Function, pp. 44-49
2.2 Powers and Polynomials, pp. 50-57
2.3 The Slope and the Tangent Line, pp. 58-63
2.4 Derivative of the Sine and Cosine, pp. 64-70
2.5 The Product and Quotient and Power Rules, pp. 71-77
2.6 Limits, pp. 78-84
2.7 Continuous Functions, pp. 85-90

3: Applications of the Derivative, pp. 91-153

3.1 Linear Approximation, pp. 91-95
3.2 Maximum and Minimum Problems, pp. 96-104
3.3 Second Derivatives: Minimum vs. Maximum, pp. 105-111
3.4 Graphs, pp. 112-120
3.5 Ellipses, Parabolas, and Hyperbolas, pp. 121-129
3.6 Iterations x[n+1] = F(x[n]), pp. 130-136
3.7 Newton’s Method and Chaos, pp. 137-145
3.8 The Mean Value Theorem and l’Hopital’s Rule, pp. 146-153

4: The Chain Rule, pp. 154-176

4.1 Derivatives by the Charin Rule, pp. 154-159
4.2 Implicit Differentiation and Related Rates, pp. 160-163
4.3 Inverse Functions and Their Derivatives, pp. 164-170
4.4 Inverses of Trigonometric Functions, pp. 171-176

5: Integrals, pp. 177-227

5.1 The Idea of an Integral, pp. 177-181
5.2 Antiderivatives, pp. 182-186
5.3 Summation vs. Integration, pp. 187-194
5.4 Indefinite Integrals and Substitutions, pp. 195-200
5.5 The Definite Integral, pp. 201-205
5.6 Properties of the Integral and the Average Value, pp. 206-212
5.7 The Fundamental Theorem and Its Consequences, pp. 213-219
5.8 Numerical Integration, pp. 220-227

6: Exponentials and Logarithms, pp. 228-282

6.1 An Overview, pp. 228-235
6.2 The Exponential e^x, pp. 236-241
6.3 Growth and Decay in Science and Economics, pp. 242-251
6.4 Logarithms, pp. 252-258
6.5 Separable Equations Including the Logistic Equation, pp. 259-266
6.6 Powers Instead of Exponentials, pp. 267-276
6.7 Hyperbolic Functions, pp. 277-282

7: Techniques of Integration, pp. 283-310

7.1 Integration by Parts, pp. 283-287
7.2 Trigonometric Integrals, pp. 288-293
7.3 Trigonometric Substitutions, pp. 294-299
7.4 Partial Fractions, pp. 300-304
7.5 Improper Integrals, pp. 305-310

8: Applications of the Integral, pp. 311-347

8.1 Areas and Volumes by Slices, pp. 311-319
8.2 Length of a Plane Curve, pp. 320-324
8.3 Area of a Surface of Revolution, pp. 325-327
8.4 Probability and Calculus, pp. 328-335
8.5 Masses and Moments, pp. 336-341
8.6 Force, Work, and Energy, pp. 342-347

9: Polar Coordinates and Complex Numbers, pp. 348-367

9.1 Polar Coordinates, pp. 348-350
9.2 Polar Equations and Graphs, pp. 351-355
9.3 Slope, Length, and Area for Polar Curves, pp. 356-359
9.4 Complex Numbers, pp. 360-367

10: Infinite Series, pp. 368-391

10.1 The Geometric Series, pp. 368-373
10.2 Convergence Tests: Positive Series, pp. 374-380
10.3 Convergence Tests: All Series, pp. 325-327
10.4 The Taylor Series for e^x, sin x, and cos x, pp. 385-390
10.5 Power Series, pp. 391-397

11: Vectors and Matrices, pp. 398-445

11.1 Vectors and Dot Products, pp. 398-406
11.2 Planes and Projections, pp. 407-415
11.3 Cross Products and Determinants, pp. 416-424
11.4 Matrices and Linear Equations, pp. 425-434
11.5 Linear Algebra in Three Dimensions, pp. 435-445

12: Motion along a Curve, pp. 446-471

12.1 The Position Vector, pp. 446-452
12.2 Plane Motion: Projectiles and Cycloids, pp. 453-458
12.3 Tangent Vector and Normal Vector, pp. 459-463
12.4 Polar Coordinates and Planetary Motion, pp. 464-471

13: Partial Derivatives, pp. 472-520

13.1 Surface and Level Curves, pp. 472-474
13.2 Partial Derivatives, pp. 475-479
13.3 Tangent Planes and Linear Approximations, pp. 480-489
13.4 Directional Derivatives and Gradients, pp. 490-496
13.5 The Chain Rule, pp. 497-503
13.6 Maxima, Minima, and Saddle Points, pp. 504-513
13.7 Constraints and Lagrange Multipliers, pp. 514-520

14: Multiple Integrals, pp. 521-548

14.1 Double Integrals, pp. 521-526
14.2 Changing to Better Coordinates, pp. 527-535
14.3 Triple Integrals, pp. 536-540
14.4 Cylindrical and Spherical Coordinates, pp. 541-548

15: Vector Calculus, pp. 549-598

15.1 Vector Fields, pp. 549-554
15.2 Line Integrals, pp. 555-562
15.3 Green’s Theorem, pp. 563-572
15.4 Surface Integrals, pp. 573-581
15.5 The Divergence Theorem, pp. 582-588
15.6 Stokes’ Theorem and the Curl of F, pp. 589-598

16: Mathematics after Calculus, pp. 599-615

16.1 Linear Algebra, pp. 599-602
16.2 Differential Equations, pp. 603-610
16.3 Discrete Mathematics, pp. 611-615

Agora aqui estão os links

Chapter 1 – complete (PDF – 4.1 MB)

Chapter 2 – complete (PDF – 4.3 MB)

Chapter 3 – complete (PDF – 5.9 MB)

Chapter 4 – complete (PDF – 2.0 MB)

Chapter 5 – complete (PDF – 4.8 MB)

Chapter 6 – complete (PDF – 4.9 MB)

Chapter 7 – complete (PDF – 2.6 MB)

Chapter 8 – complete (PDF – 3.4 MB)

Chapter 9 – complete (PDF – 1.7 MB)

Chapter 10 – complete (PDF – 2.9 MB)

Chapter 11 – complete (PDF – 4.0 MB)

Chapter 12 – complete (PDF – 2.2 MB)

Chapter 13 – complete (PDF – 4.9 MB)

Chapter 14 – complete (PDF – 2.5 MB)

Chapter 15 – complete (PDF – 4.3 MB)

Chapter 16 – complete (PDF – 1.8 MB)
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Este livro tem a matemática mais básica talvez a um nível do 12º ano português , primeiros anos da universidade ).

 
 

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É também acompanhado de um guia de estudo que tem os problemas resolvidos do  livro acima mencionado.

Chapter 1 – (PDF)

Chapter2 – (PDF)

Chapter 3- (PDF)

Chapter 4- (PDF)

Chapter 5- (PDF)

Chapter 6-(PDF)

Chapter 7-(PDF)

Chapter 8-(PDF)

Chapter 9-(PDF)

Chapter 10 -(PDF)

Chapter 11- (PDF)

Chapter 12-(PDF)

Chapter 13 -(PDF)

Chapter 14 -(PDF)

Chapter 15 – (PDF)

É também acompanhado de um guia para o professor

Chapter 1 -(PDF)

Chapter 2 – (PDF)

Chapter 3 – (PDF)

Chapter 4 – (PDF)

Chapter 5 – (PDF)

Chapter 6 – (PDF)

Chapter 7 – (PDF)

Chapter 8 – (PDF)

Chapter 9- (PDF)

Chapter 10 – (PDF)

Chapter 11- (PDF)

Chapter 12 – (PDF)

Chapter 13 – (PDF)

Chapter 14 – (PDF)

Chapter 15 –   (PDF)

Chapter 16  -(PDF)

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