differential calculus formulas pdf
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You may need to revise this concept before continuing. 1.1 An example of a rate of change: velocity third order respectively. Trigonometry cos0 = sin π 2 = 1, sin0 = cos π 2 = 0, cos2 θ+sin2 θ = 1, cos(−θ) = cosθ, sin(−θ) = −sinθ, cos(A+B) = cosAcosB−sinAsinB, cos2θ = cos2 θ−sin2 θ, Integral Calculus Formula Sheet Derivative Rules: 0 d c dx nn 1 d xnx dx sin cos d x x dx sec sec tan d x xx dx tan sec2 d x x dx cos sin d x x dx csc csc cot d x xx dx cot csc2 d … Differential calculus is about describing in a precise fashion the ways in which related quantities change. Integrals 5. A basic understanding of calculus is required to undertake a study of differential equations. You are strongly encouraged to do the included Exercises to reinforce the ideas. Limits and Derivatives 2. 0.1The trigonometric functions The Pythagorean trigonometric identity is sin2 x +cos2 x = 1, and the addition theorems are sin(x +y) = sin(x)cos(y)+cos(x)sin(y), cos(x +y) = cos(x)cos(y)−sin(x)sin(y). Elementary Differential and Integral Calculus FORMULA SHEET Exponents xa ¢xb = xa+b, ax ¢bx = (ab)x, (xa)b = xab, x0 = 1. Therefore, the order of these equations are 1, 2 and 3 respectively. Important mathematical terms are in boldface; key formulas and concepts are boxed and highlighted (). Basic Properties and Formulas If fx and g x are differentiable functions (the derivative exists), c and n are any real numbers, 1. cf cf x To proceed with this booklet you will need to be familiar with the concept of the slope (also called the gradient) of a straight line. absolutely not intended to be a substitute for a one-year freshman course in differential and integral calculus. To This zero chapter presents a short review. Applications of Differentiation 4. Applications of Integration Professor: Dr. Mohammad Shakil C0-Author: Jeongmin Correa Mathematics Department Logarithms lnxy = lnx+lny, lnxa = alnx, ln1 = 0, elnx = x, lney = y, ax = exlna. BASIC CONCEPTS OF DIFFERENTIAL AND INTEGRAL CALCULUS 8.3 By definition x x 2x x ( x) x lim x (x x) x lim x f(x x) f(x) f(x) lim dx d 2 2 2 x 0 2 2 x 0 x 0 = lim (2x x) 2x 0 2x x 0 Thus, derivative of f(x) exists for all values of x and equals 2x at any point x. 9.2.2 Degree of a differential equation To study the degree of a differential equation, the key point is that the differential equation must be a polynomial equation in derivatives, i.e., y′, y″, y″′ etc. Calculus I Formulas MAC 2311 1. Differentiation rules 3.
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