COURSE UNIT TITLE

: MATHEMATICS APPLICATIONS IN PHYSICS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
LMÖ 1008 MATHEMATICS APPLICATIONS IN PHYSICS COMPULSORY 2 0 0 3

Offered By

Mathematics Teacher Education

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSISTANT PROFESSOR YUSUF ERKUŞ

Offered to

Mathematics Teacher Education

Course Objective

The main purpose of this course is to show how the basic mathematical concepts (derivative, integral, vectors, multivariable functions, etc.) that the prospective teachers learned in Analysis I and Analysis II courses are used and applied in the basic subjects of classical physics (mechanics, gravity, simple electromagnetism). The course aims to reveal how effective abstract mathematical tools are in understanding and solving concrete physical problems by emphasizing the strong relationship between mathematics and physics. In this way, it is aimed to increase the students' motivation for mathematics and to provide them with the ability to relate mathematical concepts to physical examples when teaching in the future.

Learning Outcomes of the Course Unit

1   Express physical concepts (speed, acceleration, force, work, energy, potential, area, etc.) using mathematical language (functions, equations, vectors).
2   To apply the derivative and integral applications of single and multivariable functions to basic physical problems (kinematics, work-energy, center of mass, etc.).
3   Formulate basic physical laws (simple forms of Newton's Laws ) using vector quantities (position, velocity, force, area) .
4   Solve simple mathematical models (equations) based on basic physical laws or definitions using knowledge of Analysis I and II and interpret the results physically.
5   To calculate basic physical quantities (center of mass, moment of inertia, electric field, electric potential - for simple geometries) caused by mass or charge distributions using integrals.
6   Appreciate the role and importance of mathematical tools in the development of physics.
7   Gain the ability to relate abstract mathematical concepts to concrete, real-world examples.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Introduction and Basic Concepts Physics-Mathematics Relationship. Physical Quantities. Vectors and Scalars : Vector operations (addition, subtraction, scalar multiplication, vector product ) - Vector Knowledge Application.
2 Mathematics of Linear Motion ( Kinematics - 1 Dimension) Position, Velocity, Acceleration: Definitions. Instantaneous Velocity (derivative of position), Instantaneous Acceleration (derivative of velocity): Application of Derivatives. Calculating Velocity and Position: Integration of acceleration and velocity. Derivative/integration of equations of motion with constant acceleration.
3 Mathematics of Vector Motion ( Kinematics - 2/3 Dimensions) Position, Velocity, Acceleration Vectors. Application of Derivative and Integral of Vector Valued Functions. Projectile Motion: Derivative/Integral Analysis on Vector Components.
4 Force and Newton's Laws Newton's Second Law - Vector Form. Force and Momentum - Application of Derivatives. Setting up Simple Equations of Motion (setup only and verification of solutions by differentiation).
5 Work and Energy (One Dimension) Constant Force Work. Variable Force Work: Application of Definite Integral. Kinetic Energy. Work-Energy Theorem: Proof Using Definite Integral.
6 Work and Energy (Multidimensional) and Potential Energy Constant Force Work: Application of Scalar Multiplication. Variable Force Work: Introduction to the Concept of Path Integral (simple conservative fields). Potential Energy Definition: Application of Definite Integral. Force = - Gradient - Application of Partial Derivatives and Gradient.
7 Conservation of Energy and its Applications Conservation of Mechanical Energy. Potential Energy Curves and Finding Force from Graphs: Application of Derivatives (Equilibrium Points). Energy Conservation Problems.
8 General review, course evaluation, midterm exam
9 Momentum and Thrust Definition of Momentum. Impulse: Application of the Definite Integral of Force with Time. Impulse-Momentum Theorem. Conservation of Momentum (conceptual).
10 Fundamentals of Rotational Motion (Selected Topics) Angular Position/Velocity/Acceleration: Linear analogy, Derivative/Integral relationships. Moment of Inertia: Simple Single, Double or Triple Integral Calculations for mass distributions. Torque and Angular Momentum: Application of Vector Multiplication.
11 Gravity Newton's Law of Gravitation. Gravitational Field: Superposition of Point Mass, Integral Calculations for Simple Mass Distributions (rod, ring axis). Potential Energy: Integral Calculations for Simple Distributions. Area = -Gradient.
12 Electric Field and Potential (Simple Distributions) Coulomb's Law, Point Charge Field. Field of Continuous Charge Distributions: Integral Calculations for Simple Geometries (rod, ring, disk axis). Electric Potential: Integral Calculations for Simple Charge Distributions.
13 Relation between Electric Field and Potential, Simple Flux Area = -Gradient. Definition of Electric Flux: Introduction to Scalar Multiplication and Simple Surface Integral - Highly symmetric or flat surfaces.
14 Gauss's Law (Integral Form - High Symmetry Cases) Definition of Gauss's Law: Flux through a closed surface - Surface Integral Form. Applications for Highly Symmetry Cases (sphere, cylinder, plane): Transformation of Surface Integral to Simple Algebraic Expression and Area Calculus.
15 Final Exam

Recomended or Required Reading

Özmantar, M.F., Bingölbali, E., Akkoç, H. (2008). Matematiksel Kavram Yanılgıları ve Çözüm Önerileri, Pegem Akademi Yayınları, Ankara.
Bingölbali, E., Özmantar, M.F. (2009). Ilköğretimde Karşılaşılan Matematiksel Zorluklar ve Çözüm Önerileri, Pegem Akademi Yayınları, Ankara.

Planned Learning Activities and Teaching Methods

Lecture: Presentation of basic physical concepts within their mathematical framework.

Sample Solution: Solving physical problems step by step with mathematical methods and explaining the physical meanings of mathematical steps.

Question-Answer and Discussion: Addressing points that students have difficulty understanding or different solution approaches.

Problem Solving Sessions: Encouraging students to actively solve physics problems using mathematical methods during class or in additional sessions.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 VZ Midterm
2 FN Semester final exam
3 BNS BNS Student examVZ * 0.40 + Student examFN * 0.60
4 BUT Make-up note
5 BBN End of make-up grade Student examVZ * 0.40 + Student examBUT * 0.60


Further Notes About Assessment Methods

None

Assessment Criteria

Assessment of students is measured by midterm and final exams in line with the learning outcomes.

Language of Instruction

Turkish

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

yusuf.erkus@deu.edu.tr

Office Hours

It will be announced at the beginning of the semester.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 2 26
Preparations before/after weekly lectures 13 1 13
Preparation for midterm exam 1 15 15
Preparation for final exam 1 15 15
Midterm 1 3 3
Final 1 3 3
TOTAL WORKLOAD (hours) 75

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14PO.15PO.16PO.17PO.18
LO.1131132541444323
LO.2131232551445434
LO.3131232541445434
LO.4141243551555535
LO.5131232551445434
LO.6142145531434535
LO.7131132541444323

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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