No 1. 2. 3. 4. 5. 6. 7. 8. Code: UCCM1153 Status: Credit Hours: 3 Semester and Year Taught: Information on Every Subject Name of Subject: Introduction to Calculus and Applications Pre-requisite (if applicable): None Mode of Delivery: Lecture and Tutorial Valuation: Course Work Final Examination 40% 60% 9. 10. Teaching Staff: Objective(s) of Subject: • Review the notion of function and its basic properties. • Understand the concepts of derivatives. • Understand linear approximations. •
Premium Derivative
Calculus is the mathematical study of change‚[1] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. It has two major branches‚ differential calculus (concerning rates of change and slopes of curves)‚ and integral calculus (concerning accumulation of quantities and the areas under curves); these two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental
Premium Derivative Calculus
How the calculus was invented? Calculus‚ historically known as infinitesimal calculus‚ is a mathematical discipline focused on limits‚ functions‚ derivatives‚ integrals‚ and infinite series. Ideas leading up to the notions of function‚ derivative‚ and integral were developed throughout the 17th century‚ but the decisive step was made by Isaac Newton and Gottfried Leibniz. Publication of Newton’s main treatises took many years‚ whereas Leibniz published first (Nova methodus‚ 1684) and the whole
Premium Calculus Mathematics Gottfried Leibniz
Calculus is the mathematical study of change‚[1] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. It has two major branches‚ differential calculus (concerning rates of change and slopes of curves)‚ and integralcalculus (concerning accumulation of quantities and the areas under curves); these two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental
Premium Derivative
1. ht= -4.9t2+ 450‚ where t is the time elapsed in seconds and h is the height in metres. a) Table of Values t(s) | h(t) (m) | 0 | ht= -4.9(0)2+ 450= 450 | 1 | ht= -4.9(1)2+ 450= 445.1 | 2 | ht= -4.9(2)2+ 450= 430.4 | 3 | ht= -4.9(3)2+ 450= 405.9 | 4 | ht= -4.9(4)2+ 450=371.6 | 5 | ht= -4.9(5)2+ 450=327.5 | 6 | ht= -4.9(6)2+ 450= 273.6 | 7 | ht= -4.9(7)2+ 450= 209.9 | 8 | ht= -4.9(8)2+ 450= 136.4 | 9 | ht= -4.9(9)2+ 450=53.1 | 10 | ht= -4.9(10)2+ 450= -40 |
Premium Derivative Velocity Calculus
History of Differential Calculus Universidad Iberoamericana September 20‚ 2013 Ever since men felt the need to count‚ the history of calculus begins‚ which together with Mathematics is one of the oldest and most useful science. Since men felt that need for counting objects‚ this need led to the creation of systems that allowed them to maintain control of their properties. They initially did it with the use of fingers‚ legs‚ or stones. But as humans continued developing
Premium Calculus Mathematics Derivative
1. Physical Properties of Water and Ice 1. Molecular Weight: A. 18.01528 g/mol Water‚ Molar mass Triple Point The temperature and pressure at which solid‚ liquid‚ and gaseous water coexist in equilibrium is called the triple point of water. This point is used to define the units of temperature (the kelvin‚ the SI unit of thermodynamic temperature and‚ indirectly‚ the degree Celsius and even the degree Fahrenheit). As a consequence‚ water’s triple point temperature is a prescribed value rather
Free Thermodynamics Temperature Water
SOLUTIONS TO SUGGESTED PROBLEMS FROM THE TEXT PART 2 3.5 2 3 4 6 15 18 28 34 36 42 43 44 48 49 3.6 1 2 6 12 17 19 23 30 31 34 38 40 43a 45 51 52 1 4 7 8 10 14 17 19 20 21 22 26 r’(θ) = cosθ – sinθ 2 2 cos θ – sin θ = cos2θ z’= -4sin(4θ) -3cos(2 – 3x) 2 cos(tanθ)/cos θ f’(x) = [-sin(sinx)](cosx) -sinθ w’ = (-cosθ)e y’ = cos(cosx + sinx)(cosx – sinx) 2 T’(θ) = -1 / sin θ x q(x) = e / sin x F(x) = -(1/4)cos(4x) (a) dy/dt = -(4.9π/6)sin(πt/6) (b) indicates the change in depth of water (a) Graph at
Premium 1980 1979 1983
CALCULUS Calculus is the study of change which focuses on limits‚ functions‚ derivaties‚ integrals‚ and infinite series. There are two main branches of calculus: differential calculus and integral calculus‚ which are connected by the fundamental theorem of calculus. It was discovered by two different men in the seventeenth century. Gottfried Wilhelm Leibniz – a self taught German mathematician – and Isaac Newton - an English scientist - both developed calculus in the 1680s. Calculus is used in a
Premium Calculus Derivative Gottfried Leibniz
tool for describing the real world in mathematical terms. A function can be represented by an equation‚ a graph‚ a numerical table or a verbal description. In this section we are going to get familiar with functions and function notation. MAT133 Calculus with Analytic Geometry II Page 1 An equation is a function if for any x in the domain of the equation‚ the equation yields exactly one value of y. The set of values that the independent variable is allowed to assume‚ i.e.‚ all possible
Premium Exponential function Natural logarithm