Nguồn ngoài
Street-Fighting Mathematics
An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions.
- Tác giả
- Sanjoy Mahajan
- Nhà xuất bản
- Olin College of Engineering
- Nguồn
- LibreTexts
- Giấy phép
- CC BY-NC-SA
- Ngôn ngữ
- EN
- Danh mục
- Khoa học cơ bản
Mục lục· 38 mục
- 01: Dimensions
- 1.01: Economics- The power of multinational corporations
- 1.02: Newton mechanics- Free fall
- 1.03: Guessing Integrals
- 1.04: Summary and further problems
- 02: Easy Cases
- 2.01: Gaussian Integral Revisited
- 2.02: Plane Geometry - The Area of an Ellipse
- 2.03: Solid Geometry - The Volume of a Truncated Pyramid
- 2.04: Fluid mechanics- Drag
- 2.05: Summary and further problems
- 03: Lumping
- 3.01: Estimating populations - How many babies
- 3.02: Estimating Integrals
- 3.03: Estimating Derivatives
- 3.04: Analyzing differential equations- The spring-mass system
- 3.05: Predicting the Period of a Pendulum
- 3.06: Summary and Further Problems
- 04: Picture Proofs
- 4.01: Adding Odd Numbers
- 4.02: Arithmetic and Geometric Means
- 4.03: Approximating the logartihm
- 4.04: Bisecting a Triangle
- 4.05: Summing series
- 4.06: Summary and Further Problems
- 05: Taking out the big part
- 5.01: Multiplication using one and few
- 5.02: Fractional changes and low-enthropy expressions
- 5.03: Fractional changes with general exponents
- 5.04: Successive approximation- How deep is the well
- 5.05: Daunting Trigonometric Integral
- 5.06: Summary and further problems
- 06: Analogy
- 6.01: Spatial Trigonometry- The Bond Angle in Methane
- 6.02: Topology- How many regions
- 6.03: Operators - Euler-MacLaurin summation
- 6.04: Tangent roots- A daunting transcendental sum
- 6.05: Bon Voyage