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# Follow-up Course in Technical Mathematics

Structure Type: Study unit IT00BL15 IT 2022 Bachelor of Engineering 2 (2023-2024) Autumn 5 cr Mäkelä, Jarmo English

## Courses During the Academic Year 2023-2024

Impl.Group(s)Study TimeTeacher(s)LanguageEnrolment
3001IT2022-2, IT2022-2A, IT2022-2B2023-08-28 – 2023-12-16Jarmo MäkeläFinnish2023-08-01 – 2023-09-06

## Learning Outcomes

At the end of the course the student has a good knowledge on the differential and integral calculus of single-variable functions. The student also knows the basics of ordinary differential equations and series, and possesses rudimentary knowledge on multivariable analysis.

The total workload of the student during the course is approximately 130 hours.

## Prerequisites / Recommended Optional Courses

Basics of Technical Mathematics

## Contents

1) Limit and continuity of a function. 2) The derivative of a function and its geometrical interpretation. 3) Rules of differentiation. 4) Partial derivative and differentials. 5) Optimization of single-variable functions. 6) Optimization of multivariable functions. 7) Lagrange's method of undetermined variables. 7) Inverse function differentiation. 8) Inverse trigonometric functions and their derivatives. 9) Implicit differentiation. 9) Indefinite integral. 10) Definite integral and its geometrical interpretation. 11) Methods of integration: Integration by parts, integration by substitution, integration by means of partial fractions. 12) Hyperbolic functions and their properties. 13) Trigonometric and hyperbolic subsititutions in indefinite integrals. 14) The volume of the solid of revolution. 15) The length of a curve. 16) The sheet area of the surface of revolution. 17) The center of gravity of a plate. 18) Surface integral and its geometrical interpretation. 19) Evaluation of surface integrals in curvilinear coordinates. 20) First-order differential equations. 22) Second-order linear differential equation with constant coefficients. 23) Laplace transform. 24) Inverse Laplace transform. 25) Solution of linear differential equations by means of Laplace transforms. 26) Series. 27) Arithmetic and geometrical series. 28) Power series: Maclaurin series. 29) Binomial series. 30) Evaluation of indefinite integrals by means of power series. 31) Elements of Fourier series.

## Recommended or Required Reading and Other Learning Resources/Tools

G. James: Engineering Mathematics (recommended reading)

## Mode of Delivery / Planned Learning Activities and Teaching Methods

The course consists of lectures and exercise classes.

## Assessment Criteria

The possible grades obtainable from the course are 1, 2, 3, 4, 5.

1: The student knows the basic concepts of the course

2: The student knows about one-half of the topics taught on the course, and is able to solve simple problems

3: The student is able to solve pretty challenging problems and knows the concepts of the course

4: The student knows more or less the topics learned in the course

5: The sudent knows everything taught in the course.

## Assessment Methods

There will be two exams in the course. The grade is determined by the total number of the points obtained from the exams. In addition, the sudent must solve a given number of exercise problems.