Module Requisites and Incompatibles Incompatibles:ĪCM00010 - Intro to Mechanics, ACM00020 - Applied Maths: Methods & Appli, ACM10010 - Mathematical ModellingI, ACM10020 - Mathematical Modelling II, ACM10030 - Mechanics & Special Relativity, ACM10070 - Math Modelling in the Sciences, ACM10080 - Intro to Applied & Comp Math, ECON10030 - Intro Quantitative Economics, MATH00010 - Introduction to Mathematics, MATH10030 - Maths for Business, MATH10050 - Linear Algebra & Geom, MATH10060 - Diff & Integral Calc, MATH10070 - Introduction to Calculus, MATH10080 - Calculus & Statistics, MATH10120 - Linear Algebra Apps to Econ, MATH10140 - Advanced Calculus (E&F), MATH10230 - Mathematics for Agriculture I, MATH10240 - Mathematics for Agriculture II, MATH10280 - Linear Algebra in the Phys.Sci, MATH10290 - Linear Algebra for Science, MATH10300 - Calculus in the Math. Interval of convergence, radius of convergence for a power seriesĪpplications of Differential Equations using Separation of VariablesĪpplications of Differential Equations using Integrating Factor General solution using Integrating factorĪlternating series test and Comparison series test Linear first order differential equations. functions $\sin^ (Formulae provided on question sheet)įirst order differential equations with separable variables Trigonometric functions $\sin x$ and $\cos x$ Mechanical and geometrical interpretation of derivatiīasic rules of differentiation (sum, difference, product, quotient, chain rule) Computing the limit by multiplying with the rational conjugateĭefinition. Geometric criteria for bijective and inverse functions Indicative Module Content:ĭefinition of a function bijective and inverse functions Solve first order linear differential equations. ![]() Obtain the expansion for MacLaurin and Taylor series of a function of a single variable. Determine the Interval the Convergence of a power series. Calculate definite and indefinite integrals. Use calculus to find local extrema of a function of one variable and apply these methods to optimisation problems. Display knowledge of the properties of polynomial and rational functions, trigonometric functions and their inverses, exponential, logarithmic and hyperbolic functions. Calculate derivatives via implicit and logarithmic differentiation. On completion of this module students should be able to:1. Differential equations: first order linear equations with constant coefficients. MacLaurin and Taylor series of a function of one variable. Geometric series, Ratio Test, Harmonic series. Applications of integration: area under the curve, volume of a solid, length of a graph, surface area. ![]() 6.Indefinite and definite integrals, the fundamental theorem of calculus, integration by parts, integration by substitution and the method of partial fractions. Applications of differentiation: maxima and minima, second order derivative test. Hyperbolic functions and their inverses 5. Differentiation: Notion of derivative, product and quotient rules, derivatives of polynomial functions, review of trigonometry, derivatives of trigonometric functions and their inverses, chain rule, implicit and logarithmic differentiation, higher order derivatives. Limits: Notion of a limit, statements of basic limit theorems.3. ![]() It provides an introduction to differential and integral calculus of functions of one variable, and to differential equations. This is a mathematics module designed for engineering students. MATH10250 Introduction to Calculus for Engineers Academic Year 2023/2024
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