As a teacher of mathematics and physics in high school I used to prepare what to say in class with handwritten notes.
During my latest teaching spell I rewrote the notes in a more readable form, from pencil to felt pen so that I could
scan them and make them available for the students after each lecture. The whole procedure was quite inefficient, writing new notes all the time
instead of building on and modifying work from courses that I had taught before.
I decided to adapt to a digital era and make digital notes for each course that I could then use as a base to start from.
The present system in Sweden is based on courses.
During my time in Ystad I taught Math 1 and 2 for Science students and Physics 1 for Technology students.
Those notes I just rewrote without modification.
For the other courses Ma 3,4,5 and Ph 2 I have made new material to cover theory lessons.
Since my teaching is in Swedish the material was first made in Swedish and later translated to English,
so there is bound to be remnants of Swedish words and grammar hera and there in the English text.
To use the Geogebra files, go to this link
and install GeoGebra Classic 6.
Courses
Eng Lectures Swe
GeoGebra - Lab
Ma 1
------------------------- Choose a lecture -------------------------
Lectures
Index
01 - Introduction
02 - Arithmetic - Integers
03 - Arithmetic - Number systems
04 - Aritmethic - Calculator Sign rules Fractions
05 - Arithmetic - Cardinal number & Decimal fraction
06 - Arithmetic - Decimals & Significant digits
07 - Arithmetic - Square roots
08 - Arithmetic - Powers part 1
09 - Arithmetic - Powers part 2 and Powers of 10
10 - Arithmetic - Scientific notation and Prefixes
11 - Arithmetic - Number systems in other bases
12 - Arithmetic - Decimals in fractions Speed Units
13 - Arithmetic - Change of base
14 - Arithmetic - Problem solving
15 - Percentage - Basics & Percentage points
16 - Percentage - Percentage multiplier
17 - Percentage - Repeated change
18 - Percentage - Exercises on percentage
19 - Percentage - Loans and Amortizations
20 - Percentage - Tax Vat Index
21 - Percentage - Repetition
22 - Percentage and Arithmetic - Repetition
23 - Powers and Problem solving
24 - Algebra - Terminology and Simplification
25 - Algebra - Factoring
26 - Algebra - Linear equations
27 - Algebra - Solution of equations
28 - Algebra - Solving problems
29 - Algebra - Test
30 - Algebra - Inequalities
31 - Algebra - Power equations
32 - Algebra - Formulas
33 - Algebra - Patterns
34 - Algebra - Manipulating formulas
35 - Algebra - Repetition
36 - Repetition - Decimal expansion and Patterns
37 - Repetition - Arithmetic Percentage Algebra
38 - Geometry - History and Terms
39 - Geometry - Exercise and The Koch snowflake
40 - Geometry - Area Volume Units
41 - Geometry - Cone and Ballt
42 - Geometry - History and Angles
43 - Geometry - Exercises
44 - Geometry - Similarity and Pythagoras theorem
45 - Geometry - Trigonometry
46 - Geometry - Exercise Trigonometry
47 - Geometry - Repetition trigonometry
48 - Geometry - Vectors
49 - Geometry - Coordinate systemsm
50 - Geometry - Repetition
51 - Probability - Concepts
52 - Probability - Outcome and Tree diagrams
53 - Probability - Linked trials
54 - Probability - Complementt and Combinatorics
55 - Statistics - Averages and Diagrams
56 - Geogebra - Introduction
57 - Programming - Introduction Python
58 - Functions - Concepts and Coordinate systems
59 - Functions - Geogebra
60 - Functions - Df Vf Proportionality
61 - Funktioner - Linjära modeller
61 - Functions - Linear models
63 - Functions - Exercises with Geogebra
64 - Functions - Exponential function
65 - Functions - Power functions
66 - Functions - Repetition 1
67 - Functions - Repetition 2
68 - Ma1 - Repetition Arithmetics
69 - Ma1 - Repetition Percentage
70 - Ma1 - Repetition Old tests
71 - Ma1 - Repetition Algebra
72 - Ma1 - Repetition 1
73 - Ma1 - Repetition 2
---- Choose GeoGebra/Lab ----
Ma 2
------------------------- Choose a lecture -------------------------
Lectures
Index
01 - Algebra 1 - Repetition 1
02 - Algebra 1 - Function
03 - Linear models - Linear equation
04 - Linear models - Geogebra
05 - Linear models - Exercises
06 - Linear models - Linear regression
07 - System of linear eq. - System of equations
08 - System of linear eq. - Method of substitution
09 - System of linear eq. - Method of addition
10 - System of linear eq. - More than two unknowns
11 - System of linear eq. - Geogebra 3D and CAS
12 - System of linear equations - Application
13 - Algebra 2 - Polynomial and Multiplication
14 - Algebra 2 - Binomial rulesand Factoring
15 - Algebra 2 - Equations
16 - Quadratic eq. - pq-formula
17 - Quadratic eq. - Applications
18 - Quadratic eq. - Geogebra
19 - Quadratic eq. - Solving equations
20 - Quadratic eq. - Complex numbers
21 - Quadratic eq. - Complex numbers and Geogebra
22 - Quadratic functions - Graph
23 - Quadratic functions - Extrema
24 - Quadratic functions - Graph Square Completion
25 - Quadratic functions - Applications
26 - Function - Exponential and Power
27 - Half time - Repetition 1
28 - Half time - Repetition 2
29 - Half time - Repetition 3
30 - Half time - Repetition 4
31 - Logarithms - Concepts
32 - Logarithms - Logarithm rules
33 - Logarithms - History
34 - Logarithms - Applications
35 - Geometry - Angles
36 - Geometry - Circles and Inscribed angles
37 - Geometry - Similarity
38 - Geometry - Chorda Bisector Congruence
39 - Geometry - Constructions with Geogebra
40 - Geometry - Coordinate geometry
41 - Geometry - Proof using vectors
42 - Geometry - Repetition
43 - Statistics - Introduction and Geogebra
44 - Statistics - Spreadsheets Histogram Trials
45 - Statistics - Average
46 - Statistics - Spread
47 - Statistics - Standard deviation
48 - Statistics - Normal distribution
49 - Statistics - Normal distribution & Geogebra
50 - Statistics - Regression analysis
51 - Ma2 - Repetition Linear
52 - Ma2 - Programming exercise
53 - Ma2 - Repetition Algebra
54 - Ma2 - Repetition Quadratic
55 - Ma2 - Repetition Power and Exponential
56 - Ma2 - Repetition Geometry
57 - Ma2 - Repetition Statistics
---- Choose GeoGebra/Lab ----
39 - Euler line
48 - Normal distribution 1
48 - Normal distribution 2
Ma 3
------------------------- Choose a lecture -------------------------
Lectures
Index
01 - Algebra - Polynomials
02 - Algebra - Exponentiation
03 - Algebra - Roots and Absolute value
04 - Algebra - Equations with polynomials
05 - Algebra - Equations Substitution Roots
06 - Algebra - Factoring
07 - Algebra - Rational expr. Extend Reduce
08 - Algebra - Rational expr. Addition
09 - Algebra - Rational expr. Multiply & Divide
10 - Algebra - Functions
11 - Algebra - Equation of straight line
12 - Algebra - Quadratic function
13 - Algebra - Exponential and Power functions
14 - Derivative - Difference quotient and Tangent
15 - Derivative - Limit
16 - Derivative - Definition of derivative
17 - Derivative - Derivation of polynomials
17 - Derivative - Differentiation of polynomials
18 - Derivative - Applications s(t) v(t) a(t)
19 - Derivative - Power functions
20 - Derivative - History and Euler's number
21 - Derivative - Derivative of exp(kx)
22 - Derivative - Logarithms
23 - Derivative - Exponential function
24 - Derivative - Exercises
25 - Derivative - Calculator and Geogebra
26 - Derivative - Summary and Exercises
27 - Derivative - Extrema, Slope and Derivative
28 - Derivative - Graph analysis first derivative
29 - Derivative - Applications
30 - Derivative - Powers and Asymptotes
31 - Derivative - Second derivative
32 - Derivative - 2nd derivative Extrema GeoGebra
33 - Derivative - Applications
34 - Derivative - Pathological functions
35 - Integral - Primitive function
36 - Integral - Primitive function with conditions
37 - Integral - Integral
38 - Integral - Fundamental theorem of calculus
39 - Integral - Applications
40 - Trigonometry - Definitions
41 - Trigonometry - Unit circle and Symmetries
42 - Trigonometry - Geogebra
43 - Trigonometry - Area theorem
44 - Trigonometry - Law of sines
45 - Trigonometry - Law of cosines
46 - Trigonometry - Repetition
---- Choose GeoGebra/Lab ----
14 - Derivative
20 - Eulers e
31 - Graph & Derivative
40 - Trigonometry
42 - Unit circle
42 - Tangent of x
Ma 4
------------------------- Choose a lecture -------------------------
Lectures
Index
01 - Trigonometry - Introduction
02 - Trigonometry - Unit circle & Symmetries
03 - Trigonometry - Pythagorean identity
04 - Trigonometry - Angle sum identities
05 - Trigonometry - Double-angle formulae
06 - Trigonometry - Proof and Logic
07 - Trigonometry - Equations
08 - Trigonometry - Rewriting equations
09 - Trigonometry - Amplitude Period Phase
10 - Trigonometry - Modulation FM AM
11 - Trigonometry - Tangent function
12 - Trigonometry - Asinx plus Bcosx
13 - Trigonometry - Radians
14 - Trigonometry - Sector
15 - Trigonometry - Derivative of sine cosine
16 - Trigonometry - Composite functions
17 - Trigonometry - Applications
18 - Derivative - Repetition
19 - Derivative - Derivative of a product
20 - Derivative - Derivative of a quotient
21 - Derivative - Derivative of Exp and Ln
22 - Derivative - Coupled rate changes
23 - Derivative - Graphs and Derivatives
24 - Derivative - Various graphs
25 - Derivative - Asymptotes
26 - Derivative - Differential equations
27 - Derivative - DE applications
28 - Derivative - Numerical solution of DE
29 - Integral - Antiderviative & Calulus theorem
30 - Integral - Numerical methods
31 - Integral - Area between graphs
32 - Integral - Area
33 - Integral - Quantities
34 - Integral - Probability
35 - Integral - Applications and Problems
36 - Integral - Solids of revolution
37 - Integral - Solids of revolution part2
38 - Complex numbers - Introduction
39 - Complex numbers - Arithmetic
40 - Complex numbers - Complex plane
41 - Complex numbers - Polar form
42 - Complex numbers - Polar muliply & divide
43 - Complex numbers - Calculations in C-plane
44 - Complex numbers - de Moivres formula
45 - Complex numbers - Complex roots
46 - Complex numbers - Eulers formula
47 - Complex numbers - Quadratic equations
48 - Complex numbers - Polynomial division
49 - Complex numbers - Factor theorem
50 - Complex numbers - Basic theorem of algebra
51 - Complex numbers - Roots & coefficients
---- Choose GeoGebra/Lab ----
10 - Modulate 1
10 - Modulate 2
28 - Numerical ODE
28 - Epidemic
50 - Theorem 1 of algebra
Ma 5
------------------------- Choose a lecture -------------------------
Lectures
Index
01 - Combinatorics - Pigeonhole principle
02 - Combinatorics - Multiply Add and Permutations
03 - Combinatorics - Combinations
04 - Combinatorics - Probability
05 - Combinatorics - The binomial theorem
06 - Set theory - Introduction
07 - Set theory - Operations
08 - Graph theory - Graphs
09 - Graph theory - Trees
10 - Number theory - Divisibility
11 - Number theory - GCF LCM & Euclids algorithm
12 - Number theory - Congruence & Modular counting
13 - Number theory - Numbers in different bases
14 - Number theory - Computer science
15 - Sequences - Formulas and Recursion
16 - Sequences - Arithmetic and Geometric
17 - Sequences - Applications and Geogebra
18 - Proof - Proof by induction
19 - Differentiation - Repetition
20 - Differentiation - Derivative & Linear approx.
21 - Differentiation - Coupled changes
22 - Differentiation - Extrema
23 - Integration - Repetition
24 - Integration - Partial integration
25 - Integration - Volume with disc method
26 - Integration - Volume with shell method
27 - Integration - Generalized integrals
28 - Integration - Arc length Surface & Centre
29 - Diff. eq. - Introduction
30 - Diff. eq. - Homogeneous solution for order 1
31 - Diff. eq. - Particular solution of order 1
32 - Diff. eq. - Slope field
33 - Diff. eq. - Applications
34 - Diff. eq. - Numerical ODE and Epidemics
35 - Diff. eq. - Homogeneous solution for order 2
36 - Diff. eq. - Particular solution of order 2
37 - Diff. eq. - Separable differential equations
38 - Diff. eq. - Integrating factor
39 - Diff. eq. - Homogeneous solution of order n
40 - Diff. eq. - Difference equations
---- Choose GeoGebra/Lab ----
Theorem 1 of algebra
Ph 1
------------------------- Choose a lecture -------------------------
Lectures
Index
01 - Introduction - Physics History Measurement
02 - Introduction - SI-system Prefix
03 - Motion - Position and Velocity
04 - Motion - Repetition and Dimensional analysis
05 - Motion - Relative movement & instant velocity
06 - Motion - Velocity and s-t diagram
07 - Motion - Exercises
08 - Motion - Acceleration
09 - Motion - v-t Diagram
10 - Motion - Constant acceleration
11 - Motion - Exercises
12 - Force - The concept of Force and Law 1
13 - Force - Newtons 2nd law
14 - Force - Newtons 3rd law
15 - Force - Exercise Bouncing ball
16 - Force - Demo with air cushion track
17 - Force - Forces and Force fields
18 - Force - Springs Friction and Sloping planes
19 - Force and Motion - Repetition 1
20 - Force and Motion - Repetition 2
21 - Force and Motion - Repetition 3
22 - Energy - Conversion and Work
23 - Energy - Work and Potential energy
24 - Energy - Kinetic energy & Energy conservation
25 - Energy - Power and Efficiency
26 - Energy - Exercises
27 - Momentum - Momentum and Impulse
28 - Momentum - Collision
29 - Energy and Momentum - Repetition
30 - Energy and Momentum - Exercises
31 - Pressure - Definition and Units
32 - Pressure - Gas and Liquid columns
33 - Pressure - Archimedes' principle
34 - Pressure - Exercises
35 - Pressure - Ideal gas law
36 - Pressure - Exrcises on ideal gas law
37 - Thermodynamics - Temperature
38 - Thermodynamics - Inner energy & Heat capacity
39 - Thermodynamics - Exercises
40 - Thermodynamics - Phase transitions
41 - Thermodynamics - Heat capacities & Enthalpies
42 - Halftime - Repetition 1
43 - Halftime - Repetition 2
44 - Halftime Test - Content
45 - Halftime - Three exercises
46 - Thermodynamics - Repetition
47 - Thermodynamics - Green house effect
48 - Electricity - Charge and Force
49 - Electricity - Current
50 - Electricity - Voltage
51 - Electricity - Circuits
52 - Electricity - Repetition
53 - Electricity - Exercises and Emf
54 - Electricity - Electric energy transforming
55 - Electricity - Fields and Field strength
56 - Electricity - Potential
57 - Electricity - Millikan's oil drops
58 - Electricity - Repetition
59 - Electricity - Exercises
60 - Special relativity - Time dilation
61 - Special relativity - Length contraction
62 - Special relativity - Energy
63 - Special relativity - Exercises
64 - Particle physics - History
65 - Particle physics - The Standard Model
66 - Nuclear physics - Electromagnetic radiation
67 - Nuclear physics - Isotopes and Nuclides
68 - Nuclear physics - Nuclide chart & Mass defect
69 - Nuclear physics - Quantum mechanics & Chanse
70 - Nuclear physics - Particle physics
71 - Nuclear physics - Nuclear reactions
72 - Nuclear physics - Beta plus decay
73 - Nuclear physics - Activity and Half-life
74 - Nuclear physics - Dating with C-14
75 - Nuclear physics - Radiation meets matter
76 - Nuclear physics - Radiation doses
77 - Nuclear physics - Fission and Fusion
78 - Repetition - Motion Force
79 - Repetition - Mechanics
80 - Repetition - Pressure Gas Heat
81 - Repetition - Electricity
82 - Repetition - Exercises
---- Choose GeoGebra/Lab ----
Labs
Index
01 - Lab - Measurement
02 - Lab - G-acceleration
03 - Lab - Forces
04 - Lab - Newtons law
05 - Lab - Energy & Power
06 - Lab - Momentum
07 - Lab - Pressure
08 - Lab - Ideal gas law
09 - Lab - Heat & Cold
10 - Lab - Phase transition
11 - Lab - Electric circuits
12 - Lab - Resistance
13 - Lab - Nuclear physics
Ph 2
------------------------- Choose a lecture -------------------------
Lectures
Index
01 - Mechanics - Introduction
02 - Mechanics - Torque
03 - Mechanics - Torque exercises
04 - Mechanics - Circular motion
05 - Mechanics - Angular momentum
06 - Mechanics - History and Orbits
07 - Mechanics - Projectile motion
08 - Waves - Spring force and Energy
09 - Waves - Harmonic oscillator
10 - Waves - Pendulum 1
11 - Waves - Pendulum 2
12 - Waves - Pulses and Waves
13 - Waves - Standing waves in strings
14 - Waves - Sound and Standing waves
15 - Waves - Hearing and Volume
16 - Waves - Doppler effect and Beats
17 - Waves - Refraction and Diffraction
18 - Waves - Interference
19 - Electromagnetism - Electrical fields
20 - Electromagnetism - Capacitors
21 - Electromagnetism - Charge of capacitor
22 - Electromagnetism - Magnetism
23 - Electromagnetism - Magnetism & Current
24 - Electromagnetism - Coils
25 - Electromagnetism - Charge & magnetism
26 - Electromagnetism - Earth magnetic field
27 - Electromagnetism - Induction
28 - Electromagnetism - Coils & Self-inductance
29 - Electromagnetism - Alternating current
30 - Electromagnetism - Induction & Applications
31 - Electromagnetism - AC capacitors & inductors
32 - Electromagnetism - Oscillating circuit
33 - Waves & Particles - Electromagnetic radiation
34 - Waves & Particles - Interference
35 - Waves & Particles - Diffraction & Doppler effect
36 - Waves & Particles - Modulation
37 - Waves & Particles - Black-body radiation
38 - Waves & Particles - Optics
39 - Waves & Particles - Interference in thin layers
40 - Waves & Particles - Photoel. effect & Photons
41 - Waves & Particles - Compton Antiparticles paris
42 - Waves & Particles - Xrays Braggs law Crystals
43 - Waves & Particles - Particles as waves
44 - Waves & Particles - Quantum mechanics & QFT
45 - Waves & Particles - Atomic physics
46 - Waves & Particles - Atomic spectra part 1
47 - Waves & Particles - Atomic spectra part 2
48 - Astrophysics - Introduction
49 - Astrophysics - Distances
50 - Astrophysics - Spectral analysis
51 - Astrophysics - Exoplanets
52 - Astrophysics - The life of stars
53 - Astrophysics - The death of stars
54 - Astrophysics - Cosmology and Expansion
55 - Astrophysics - BigBang Nucleosynthesis CMBR
56 - Astrophysics - Cosmology beyond SM
---- Choose GeoGebra/Lab ----
10 - Pendulum
11 - Numerical pendulum
11 - Elastic pendulum
12 - Standing wave
12 - Sound
12 - Harmonics
15 - Beats
18 - Interference
37 - Planck