3.11 SMA 3152 CALCULUS II

Prerequisite: SMA 3112 Calculus I.

3.11.1 Purpose

To equip the learner with integration techniques and their applications.

3.11.2 Expected Learning Outcomes

By the end of this course, the learner should be able to;

1. State and apply the basic integration formulae and their extensions to integrate simple functions.

2. Evaluate integrals of given functions using appropriate integration techniques.

3. State the fundamental theorem of integral calculus and apply the theorem to evaluate definite integrals

4. Calculate the exact area under a curve and between curves, length of a curve, surface area and volume of common solids.

5. Define improper integrals of two kinds and test the convergence and divergence of improper integrals.

6. Evaluate the Cauchy’s principal value of the improper integral of the second kind.

7. Apply the Trapezoidal and Simpson’s rules to find area under a curve approximately.

3.11.3 Course Content

Techniques of integration: direct methods, standard substitution; algebraic, trigonometric, hyperbolic, t-method, integration by parts and partial fractions decomposition. Integration of powers of trigonometric functions. Applications of integration: kinematics including simple harmonic motion, arc length, solids of revolution; surface area and volume. Economic and financial models, in Cartesian coordinates.

Numerical integration: trapezoidal, mid-ordinate, Simpson's and prismoidal rules.

Prerequisite: SMA 3112 Calculus I.

3.11.1 Purpose

To equip the learner with integration techniques and their applications.

3.11.2 Expected Learning Outcomes

By the end of this course, the learner should be able to;

1. State and apply the basic integration formulae and their extensions to integrate simple functions.

2. Evaluate integrals of given functions using appropriate integration techniques.

3. State the fundamental theorem of integral calculus and apply the theorem to evaluate definite integrals

4. Calculate the exact area under a curve and between curves, length of a curve, surface area and volume of common solids.

5. Define improper integrals of two kinds and test the convergence and divergence of improper integrals.

6. Evaluate the Cauchy’s principal value of the improper integral of the second kind.

7. Apply the Trapezoidal and Simpson’s rules to find area under a curve approximately.

3.11.3 Course Content

Techniques of integration: direct methods, standard substitution; algebraic, trigonometric, hyperbolic, t-method, integration by parts and partial fractions decomposition. Integration of powers of trigonometric functions. Applications of integration: kinematics including simple harmonic motion, arc length, solids of revolution; surface area and volume. Economic and financial models, in Cartesian coordinates.

Numerical integration: trapezoidal, mid-ordinate, Simpson's and prismoidal rules.

- Lecturer: Gathoni Nyambura Shalyne