Game Math and Physics Basics in 2D

Course Curriculum

Chapter 1: 2D coordinate and vector concepts

Lecture 1: Displacements/distances along x

Lecture 2: Displacements/distances along y

Lecture 3: Unit vectors along each axis in 2D space

Lecture 4: Relative positions along coordinate axes

Lecture 5: World space vs. object space, part 1

Lecture 6: World space vs. object space, part 2

Lecture 7: Vector components in mathematical form

Lecture 8: Vector components in unity, 2 objects

Lecture 9: Displacements for tilted objects

Lecture 10: Displacements and scenes translations

Lecture 11: Z axis basics with physical model

Lecture 12: Effect of rotation on one object

Lecture 13: Vectors/vector components under rotations

Lecture 14: Vector components in unity, 3 objects

Lecture 15: Difference between distance and displacement vector length

Lecture 16: 0 magnitude displacements vs big distances

Lecture 17: Distance at tiny scales

Lecture 18: Angle basics in unity

Lecture 19: Magnitude and angle of displacement on unit circle

Lecture 20: Vectors from unit vectors

Lecture 21: Components from angles and length

Lecture 22: Unit vectors from math

Lecture 23: Vector addition for displacements, graphical rules

Lecture 24: Vector addition math

Lecture 25: Graphical vector subtraction

Lecture 26: Mathematical vector subtraction

Lecture 27: Midpoint of a segment

Lecture 28: Centroids of point distributions

Lecture 29: Weighted average, basic demo

Lecture 30: Weighted average, multiple objects, unity

Lecture 31: Simulation of coordinate translations, horizontal and vertical line segments

Lecture 32: Diagonal translations on coordinates

Lecture 33: 2D balance point, physical model

Lecture 34: Rotations and translations

Lecture 35: Constant speed in 2D, line segments

Lecture 36: Square roots in more detail

Lecture 37: Constant speed, diagonal movements

Lecture 38: Constant velocity in 2D, horizontal and vertical

Lecture 39: Constant velocity, slanted segments

Lecture 40: Speed vs. velocity for line motions

Lecture 41: 0 velocity

Lecture 42: Average concepts

Lecture 43: Average speed in 2D, horizonital segments

Lecture 44: Average speed, slanted segments

Lecture 45: Average velocity in 2D, horizontal segments

Lecture 46: Calculations involving speed and velocity

Lecture 47: Average velocity for slanted movements

Lecture 48: Displacement vector from given velocity

Lecture 49: Desired velocity from object to object

Lecture 50: Constant acceleration changing speed

Lecture 51: Visualizing acceleration

Lecture 52: Average acceleration

Lecture 53: Constant acceleration changing velocity

Lecture 54: Visualize acceleration

Lecture 55: Position vector

Lecture 56: Final velocity vector

Lecture 57: Basic vertical acceleration

Lecture 58: Physical introduction to forces

Lecture 59: Cancelling horizontal/vertical forces

Lecture 60: Cancelling slanted forces

Lecture 61: Cancelling four forces graphically

Lecture 62: Unbalanced forces

Lecture 63: Summation notation applied to forces

Lecture 64: Finding a missing vector graphically

Lecture 65: Finding a missing force mathematically

Lecture 66: Finding a force in a given direction

Lecture 67: Force equals mass times acceleration

Lecture 68: Velocity from force

Lecture 69: Position vector from initial position, velocity and acceleration

Lecture 70: Projectile motion summary

Lecture 71: Projectile motion specific example

Lecture 72: Decomposing projectile motion into individual functions

Lecture 73: Understanding x(t)

Lecture 74: Understanding y(t)

Chapter 2: Other Ideas

Lecture 1: Dot product basics

Lecture 2: Scalar projections with dot products

Lecture 3: Projecting velocity components with dot products along x and y axes

Lecture 4: Projecting velocity components along slanted vectors

Lecture 5: Course Summary