MATH 1100 - Fundamentals of Integral Calculus
Course Objectives
Unit 1 - Antiderivatives and Indefinite Integrals
1.1 - To find the antiderivative, or equivalently, the indefinite integral of a function.
1.2 - To find the indefinite integral of an algebraic function.
1.3 - To find the indefinite integral of exponential and logarithmic functions.
1.4 - To solve word problems using indefinite integrals.
Unit 2 - Integration by Substitution and Differential Equations
2.1 - To introduce the concept of integration by substitution.
2.2 - To learn substitution techniques.
2.3 - To use differential equations to calculate continuous compound interest.
2.4 - To calculate exponential growth and decay.
Unit 3 - Definite Integrals
3.1 - To define definite integrals and their properties.
3.2 - To evaluate definite integrals using substitution.
3.3 - To calculate the area under a curve.
3.4 - To calculate the area between a curve and the x-axis, and between two curves.
3.5 - To work with Lorenz curves to find the distribution of income.
Unit 4 - Definite Integrals and Applications
4.1 - To approximate a definite integral using the Rectangle Rule and the Fundamental Theorem
of Calculus.
4.2 - To find the average value of a continuous function.
4.3 - To evaluate probability density functions and continuous income streams.
4.4 - To evaluate surplus.
Unit 5 - Integration by Parts
5.1 - To evaluate integrals by a method called integration by parts.
5.2 - To integrate a function using a variety of methods.
5.3 - To solve word problems using mixed integration methods.
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