By Gilbert Strang
This textbook is a well-organized treatise on calculus. the writer intuitively presents designated and extensive factors enjoyable beginner’s wishes. The publication is either precious as a reference and a self-taught guide of calculus. bankruptcy 1: creation to Calculus; bankruptcy 2: Derivatives; bankruptcy three: functions of the by-product; bankruptcy four: The Chain Rule; bankruptcy five: Integrals; bankruptcy 6: Exponentials and Logarithms; bankruptcy 7: ideas of Integration; bankruptcy eight: functions of the crucial; bankruptcy nine: Polar Coordinates and complicated Numbers; bankruptcy 10: countless sequence; bankruptcy eleven: Vectors and Matrices; bankruptcy 12: movement alongside a Curve; bankruptcy thirteen: Partial Derivatives; bankruptcy 14: a number of Integrals; bankruptcy 15: Vector Calculus; bankruptcy sixteen: arithmetic after Calculus
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Additional info for Calculus
The average velocity after time t = 3 is zero. The average velocity before that time is 2. When the graph o f f has a corner, the graph of v has a jump. It is a step function. One new part of that example is the notation (dfldt or f' instead of v). Please look also at the third figure. Especially it shows At and A f . At the start, A f / A t is 2. After the stop at t = 3, all t's go to the same f ( t ) = 6 . So Af = 0 and df /dt = 0. time distance u =df/dt=f' f'(3) not defined slope undefined slope 2 t 3 3 Fig.
Notice these 2's! Question 2 What is the area under the cosine curve from t =0 to t = n/2? You can answer that, if you accept the Fundamental Theorem of Calculuscomputing areas is the opposite of computing slopes. The slope of sin t is cos t, so the area under cos t is the increase in sin t. No reason to believe that yet, but we use it anyway. From sin 0 = 0 to sin n/2 = 1, the increase is 1. Please realize the power of calculus. No other method could compute the area under a cosine curve so fast.
So why learn the chain rule? " We deal with ideas. I want to say clearly: Mathematics is not formulas, or computations, or even proofs, but ideas. The symbols and pictures are the language. The book and the professor and the computer can join in teaching it. The computer should be non-threatening (like this book and your professor)-you can work at your own pace. Your part is to learn by doing. EXAMPLE 8 A computer algebra system quickly finds 100 factorial. This is loo! = (100)(99)(98)... (1). The number has 158 digits (not written out here).