Free calculus : a liberation from concepts and proofs /
Conventional calculus is too hard and too complex. Students are forced to learn too many theorems and proofs. In Free Calculus, the author suggests a direct approach to the two fundamental concepts of calculus - differentiation and integration - using two inequalities. Regular calculus is condensed...
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| Format: | Book |
| Language: | English |
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Singapore :
World Scientific,
©2008
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Table of Contents:
- 0. Calculus in terms of images:. 0.1. Hill behavior and slope. 0.2. Hill height and slope: unconstructive tangent formula. 0.3. Review for FT. 0.4. Hillside length and slope: Pythagoras theorem. 0.5. Area and slope. 0.6. Explaining all of calculus in a single figure. 0.7. Calculus and novels
- 1. Official calculus. 1.0. A case: height and slopes. 1.1. Translating into function language. 1.2. Generalized first inequality. 1.3. Generalized second inequality. 1.4. Rules of differentiation. 1.5. Tables of derivatives and integrals. 1.6. Rules of integration. 1.7. A calculus net. 1.8. Taylor's series. 1.9. Euler's formula. 1.10. Possible generalizations
- 2. Differential equations of first order. 2.1. A simplest differential equation. 2.2. Varieties of simplest differential equation. 2.3. More general equations. 2.4. Tests for Euler's algorithm. 2.5. General Euler's algorithm
- 3. Differential equations of second order. 3.1. Initial value problems. 3.2. Eigenvalue problem. 3.3. Boundary value problem. 3.4. Weak equation. 3.5. Finite element solution and interpolation. 3.6. Generalization. 3.7. Summary
- 4. Free calculus. 4.1. Function spaces, norms, and triangle inequality. 4.2. Angle and Schwartz's inequality. 4.3. Inner product. 4.4. Orthogonality and projection. 4.5. Different inner products and norms. 4.6. Abstract calculus