MathLopedia

3,900 solved problems 17 topics 50 blogs

Solved college problems

MathLopedia is a notebook of college problems with a full written solution on every page. The collection follows a university sequence: limits, differential calculus, indefinite and definite integrals, series, ordinary and partial differential equations, complex numbers, vector geometry, elementary probability, introductory mechanics, and modeling and simulation.

A problem page starts from the statement you would meet on a homework sheet or an exam. The solution then writes the method in order: the setup, the technique, and the result, with the formulas set out so you can follow each line. The list below shows every topic and how many solved problems it holds.

Pick a topic, try one yourself, then read the steps

Choose a topic and you land on its chapters. Open one chapter, or browse the whole set. Filter by Easy, Medium, or Hard, search by problem number or by words from the statement, or open a random problem. Each problem card shows the statement first.

Work that statement on paper before you open the solution. View solution then shows the argument step by step, so you can compare your work with the write-up. The topic page also points to an easier set and a harder one when the course continues in either direction.

Create a practice test

When you want a set instead of one problem at a time, create a practice test. Choose one to three topics, or one topic and a single chapter. Then choose a difficulty and a length: 5, 10, 15, or 20 problems. Generate test builds a random exam from that pool.

The test shows statements only. Solutions stay hidden while you work. Open one solution when you mark that question attempted, or choose I’m done to reveal every solution. You can print the set, save it as a PDF, or copy a link that brings back the same test.

Calculus

Limits

61 problems

Sequences and functions, one-sided limits, continuity, and the standard ways through an indeterminate form.

Differential Calculus

636 problems

Derivatives and the rules, tangents and normals, extrema, and related rates.

Integrals

365 problems

Indefinite integrals by substitution, by parts, and the standard rational and trigonometric forms.

Definite Integrals

129 problems

The Fundamental Theorem, evaluating a definite integral, and the area it measures.

Applications of Definite Integrals

212 problems

Areas, arc length, volumes, and surfaces obtained from a definite integral.

Double Integrals

277 problems

Iterated integrals over rectangles and curved regions, and changing the order of integration.

Series

386 problems

Tests for positive and alternating terms, power series, and Taylor expansions.

Differential equations

First-Order Differential Equations

283 problems

Separable and linear equations, families of curves, and recovering an equation from its solution.

Second-Order Differential Equations

238 problems

Linear equations with constant coefficients, reduction of order, and initial values.

Systems of Differential Equations

84 problems

Coupled equations solved by elimination, and the orbits drawn in the phase plane.

Stability in Differential Equations

58 problems

Equilibria, Lyapunov stability, and the linearization that decides them.

Partial Differential Equations

169 problems

Separation of variables for the heat, wave, and Laplace equations.

Complex numbers

Complex Numbers

204 problems

Arithmetic in the plane, polar form, and the geometry of multiplication.

Geometry

Geometry

334 problems

Triangles, circles, and polygons, and the classical arguments that relate them.

Probability

Probability

146 problems

Counting, discrete and continuous distributions, and expectation.

Physics

Physics

297 problems

Kinematics, gravity, fields, and motion along a line.

Modeling and Simulations

Modeling and Simulations

21 problems

Lagrange equations for a mechanical system, the block diagram, and a numerical simulation of the motion.