Understand SI units in electric and electronic circuits, and learn voltage, current, power, and energy, then apply the passive sign convention to compute element power.

Learn the si system and its seven base quantities, with base units meter, kilogram, second, ampere, kelvin, mole, candela, and their symbols m, kg, s, A, K, mol, cd.

Explore how derived si units extend base quantities and summarize units, symbols, and formulas for frequency, force, energy, power, electric charge, electric potential, resistance, conductance, and capacitance.

Present the bipolar electric charge, the energy per unit charge that defines voltage, and its differential form dV/dQ, with W in joules and Q in coulombs, linking to current.

Define current as the rate of charge flow, I = Q / t, measured in amperes, and treat it as a continuous variable since billions of electrons flow.

Define the ideal basic circuit element as a two-terminal, nondecomposable component described by voltage or current, with standard reference directions for voltage and current.

Apply passive sign convention by choosing a reference polarity and current direction; interpret power as positive when current follows voltage drop, otherwise negative, with power equal to voltage times current.

Examine the power energy relationship and perform power and energy calculations crucial for circuit analysis, noting that one watt equals one joule per second and devices have power limits.

Explore how the algebraic sign of power depends on current direction relative to voltage drop or rise, with P = VI or P = -VI showing delivery or extraction.

Explore the algebraic sign of power through two polarity scenarios, showing P = VI yields 40 watts in each case and that positive power means the circuit absorbs energy.

Learn the symbols and behaviors of independent and dependent voltage and current sources and resistors, apply Ohm's law and Kirchhoff's laws, and perform basic power calculations in simple circuits.

Identify how electric sources convert energy, using batteries and dynamos as examples, and distinguish ideal voltage sources from ideal current sources, noting their fixed quantities and nonexistence in practice.

Classify ideal sources as independent or dependent; independent sources supply fixed voltage or current, while dependent ones rely on circuit variable. Represent independent sources with circles, dependent sources with diamonds.

Explore the four dependent sources shown by the diamond symbol: voltage-controlled voltage source, current-controlled voltage source, voltage-controlled current source, and current-controlled current source, with controlling variables and defining equations.

Define electric resistance and the resistor, and explain how collisions cause resistive heating. Learn the units ohm and siemens, and the reciprocal relation between resistance and conductance.

Learn Ohm's law, linking voltage, current, and resistance for resistors. Use the three algebraic forms V=IR, I=V/R, and R=V/I, guided by passive sign convention and the ideal resistance assumption.

Compute power absorbed by a resistor using V×I, V^2/R, or I^2R, and select the most convenient form from Ohm's law based on the available values.

Solve power calculations in circuits by applying Ohm's law to determine voltages, currents, and powers across resistors, using ground reference and polarity conventions.

Define electric circuits as a collection of circuit elements, like a battery and a light bulb, connected by wires to share current and voltage, using circuit symbols in diagrams.

Learn circuit analysis as finding voltages and currents in a circuit using element laws like Ohm's law and connection laws, Kirkos laws, with branches, nodes, and series or parallel connections.

Identify branches in circuits and analyze each element's branch current and branch voltage. Learn to label currents and voltages with element subscripts, noting polarity and direction.

Explore the reference node concept through a five-element circuit, solving for node voltages with D as the reference and then with C as the data node, verifying with branch voltages.

Explore series and parallel connections in circuits, where series shares a simple node and current remains same, while parallel shares the same pair of nodes and voltage stays the same.

Test understanding of series and parallel circuits: X1 and X2 are in series, X5 and X6 are in parallel sharing C and D; X3 is not parallel due to X4.

Identify nodes, simple nodes, loops and meshes in a six element circuit. Determine series and parallel relationships, with X1 and X2 in series and X4 and X6 in parallel.

Explore Kirchoff's current law (KCL), which states that the sum of currents entering a node equals the sum leaving, reflecting charge conservation at a junction, with a water-pipes analogy.

Apply Kirchhoff's current law to a six-element circuit by labeling nodes and solving node equations with assumed currents; positives confirm directions, negatives require reversing, as in node B.

Explore the three forms of Kirchhoff's current law, where the sum of currents at a node equals zero, using positive entering and negative leaving currents, and forms yield the result.

Apply Kirchhoff's voltage law to a circuit loop by summing voltage rises and drops. Ensure the total rises equal the total drops.

Present an example of kvl by assigning voltages and polarities, deriving six loop equations (clockwise and anticlockwise), and interpreting positive or negative results to determine unknown voltages.

Explore the three forms of the voltage loop rule, showing the algebraic sum of voltages around a loop equals zero, with rises positive, drops negative, and current direction considered.

Apply Ohm's law and Kirchhoff's laws to solve circuits, determine currents and voltages, and verify power conservation across resistors and sources.

Learn to solve circuits with dependent sources using Ohm's law, Kirchhoff's laws, and node analysis. Label nodes, choose useful loops, form two independent equations, and compute currents and voltages.

Solve a circuit with dependent sources by applying Kirchhoff's laws to two loops, determine currents and voltages, including a current-dependent voltage source; verify power conservation.

Combine series resistors into an R_eq by summing R1 through RN, since they share the same current, and verify with Ohm's law and Kirchhoff's voltage law.

Learn to identify resistors connected in parallel by sharing the same pair of nodes and compute their equivalent resistance using the reciprocal-sum formula; convert to conductance and apply two-resistor simplifications.

Learn how a voltage divider uses two resistors to derive V1 and V2 from a single supply, applying Ohm's law and noting loading and power loss.

Explore how a load in parallel with R2 alters a voltage divider's output, derive the effective resistance, and examine how tolerances affect accuracy.

Examine how ±10% resistors in a voltage divider affect the output voltage, derive the max and min Vout using R1 and R2 with Vin, and recognize tolerance-driven accuracy.

Master the node voltage method to solve circuits with fewer equations, alongside mesh current method, by identifying essential and reference nodes and deriving node voltage equations.

Apply the node voltage method to solve a circuit by identifying essential and reference nodes, formulating KCL equations, and computing node voltages V1 and V2 to determine currents and voltages.

Solve the circuit with the node voltage method by identifying essential nodes and a reference node, forming two equations, and solving for v1 and v2 using elimination or matrices.

Showcases the node voltage method on a circuit with four essential nodes to find v1, v2, and v3 using three equations and a matrix inverse.

Apply the node voltage method to a multi-source circuit with three essential nodes, derive two equations for v1 and v2, then compute five currents using Ohm's law.

Use the node voltage method to solve a two-node circuit with two voltage sources and a current source, first finding v1 and v2, then currents i1, i2, and i3.

Use the node voltage method on circuits with dependent sources, set up node and constraint equations, solve for v1, v2, and ia, and compute the power in the 5-ohm resistor.

Learn how to apply the node voltage method to circuits with dependent sources, handle essential and super nodes, and derive node equations and a constraint equation to solve voltages.

Master node voltage method with dependent sources, including super nodes and essential nodes. Apply the method to compute the power delivered by the 20 V source from node voltages.

Master simplifying algebraic fractions by canceling common factors, understanding three fraction types, and simplifying sums in the numerator to obtain a single result.

Learn to simplify fractions with different denominators by creating a common denominator through multiplication, then add the numerators to complete the expression.

Learn how to simplify fractions with different denominators by finding a common denominator XY, multiply numerators to match XY, and obtain (3Y-2X)/(XY) as the simplest form.

Compute the equivalent capacitance of capacitors in series by converting to common denominators, summing reciprocals, and flipping the result to obtain C.

Tackle five fraction problems with constants and multiple variables to simplify to the simplest form. The lesson includes steps to track solutions; revisit mistakes and avoid cheating.

Master solving linear equations by simplifying both sides, isolating the variable, and using steps such as multiplying out and moving terms across the equals sign to find y.

Work through six practice problems on algebraic linear equations, then compare your answers to the provided solutions. If your results differ, revisit your steps to strengthen understanding.

Master the four basic operators—addition, subtraction, multiplication, and division—and learn the BODMAS order of operations, including brackets and indices, to solve algebraic expressions correctly.

Explore powers and rules, showing that squaring yields a positive result for any number, with 3^2 = 9 and 3^3 = 27, and introduce square roots.

Master rounding to decimal places and significant figures, and use estimation to obtain quick, rough results and spot calculation errors in electrical engineering calculations.

Round numbers to a number of significant figures by counting from the first nonzero digit, ignoring leading zeros. Round up if next digit is five or greater; otherwise round down.

Explore fractions, decimals, and percentages as different ways to display a proportion of a whole, with examples like 1/5, 0.2, and 20% or 25% of 40 dollars.

Master ratio and proportion through examples like class gender ratios and money splits, calculate the magnitude of each part, and verify that sums match the total.

Identify irrational numbers as opposite of rational numbers; they cannot be expressed as a ratio, and decimals go on forever with no repeating pattern, denoted by B or Q prime.

Apply set theory to classify numbers using Venn diagrams, identifying natural numbers, integers, rationals, and irrationals, with examples distinguishing their relationships and types.

Explore logic about whether statements are always, sometimes, or never true, including integers as whole numbers, natural numbers, and when a square exceeds the original number, with practical examples.

Explore the basics of the coordinate system, including the x and y axes, origin, and Cartesian coordinates, and learn to locate points, measure distances, and find midpoints on a plane.

Explore the x-axis and y-axis coordinate system by identifying each point’s address as (x, y) and reach points from the origin by moving along the x-axis, then the y-axis.

Examine how a straight line is defined by y = mx + c, where m is slope and c is the y-intercept, and how to find x- and y-intercepts.

Explore slope and gradient with pictorial examples, illustrating positive, negative, and zero gradients on a straight line. Learn the gradient from two points using M = (Y2−Y1)/(X2−X1) with consistent point order.

Find the equation of a straight line from two points, including a negative component, by calculating the slope and y-intercept, illustrated with a diagram and two methods.

Derive and verify straight-line equations using coordinates, slope, and intercept to form y = mx + c, with examples y = 3 and y = 2x + 7.

Convert non-standard linear equations into standard form y = mx + c to easily read the gradient and y-intercept, since rearranging across the equals sign does not change the values.

Explore the second formula for a straight line using the point-slope form Y - Y1 = M(X - X1) and its connection to Y = MX + C.

Find the intersection of two straight lines by solving their equations simultaneously. Substitute the x-value into either equation to obtain y and verify the intersection at (2, -3).

Learn to find the intersection of two lines by plotting points and solving the equations simultaneously, using y=4x and y=-3x+7 as an example.

Practice solving parallel and perpendicular line problems using slope, intercept, and point, deriving equations and converting to standard form.

Understand how a function maps each input to a unique output, with input independent and output dependent. See f(x)=x+2 and f(x)=2x-1, shown as a straight-line graph.

Explore the graphs of common functions, including straight lines, parabolas, cubics, square roots, absolute value, reciprocals, circles, exponentials, logarithms, and sine, cosine, and tangent, with sketching from scratch.

Explore straight-line graphs and equations, focusing on slope m and y-intercept c. Learn to find x-intercepts and see how changing c shifts lines up or down while keeping the slope.

Identify whether a graph is a function by one-to-one input-output mapping, comparing y = x and y = x^3 with x = y^2 and x^2 + y^2 = 1.

Explore a library of fundamental functions, including constant, identity, linear, square, cube, square root, and reciprocal functions, with their graphs, domains, and key features.

Learn about vertical and horizontal asymptotes using the y = 1/x graph; see how the curve approaches axes and infinity without touching, and relate this to limits.

Explore how limits describe graph behavior with horizontal and vertical asymptotes as x approaches zero from the positive and negative sides, and as x tends to infinity or minus infinity.

Explore translations of graphs with vertical shifts, showing how adding three to f(x)=x^2 moves the parabola up three units and subtracting four moves it down four units while preserving shape.

Explore graph translations by plotting F(x) = x^2 to observe vertical shifts. Then examine horizontal shifts using F(x) = x^3 with x^3, x-2^3, and x+4^3.

Explore how shifting a function's graph—vertical shifts y=f(x)+k and horizontal shifts y=f(x−h) or y=f(x+h)—affects the graph, with parabola examples.

Explore translations of the parabola f(x)=x^2 by applying vertical and horizontal shifts, combine translations, compare original and shifted graphs, and observe how the center moves without changing shape.

Practice transforming a piecewise linear graph by applying horizontal and vertical scaling: compare y = f(2x) and 2f(x) to observe horizontal compression and vertical stretch.

Explore how reflections flip graphs around the x-axis and y-axis, using y = x^2 and y = sqrt(x) to show changes in points and quadrants.

Summarizes six graph manipulations, focusing on translations. Shifting the graph upward by adding A to the function (f(x)+A) yields (x, y) -> (x, y+A), while f(x+A) shifts left (x, y) -> (x-A, y).

Explore reflections across the x-axis and y-axis, where coordinates flip and remain fixed accordingly. Examine vertical and horizontal scaling by a, including F(ax) versus aF(x).

Explore parabola transformations via stretching, translation, and reflection, including horizontal shifts along the x axis and vertical shifts along the y axis, shown with y = 2x^2 and related forms.

Explore descriptive statistics for categorical and quantitative data using frequency distributions, bar charts, Pareto diagrams, and pie charts. Explore skewness, cumulative distributions, cross tabulation, and Simpson's paradox.