Calculus vs Game Theory

Calculus you can see is calculus you can learn. Calculus: Learn & Practice turns a full first-year calculus course into one clear path: build intuition with an interactive animation, follow a worked example step by step, then prove to yourself you've got it with instantly graded practice. WHAT'S INSIDE • 111 interactive concept animations — play, scrub and watch the key change happen instead of imagining it • 336 worked examples with complete solutions, visual hints and the mistakes students usually make • 1,246 practice problems graded the moment you submit, each with a full solution • Math-history stories with the original problems: Zeno's paradoxes, Archimedes' π, Fermat and Descartes' fight over tangents • Mistake tracking and mastery per concept, so you know exactly what to review • Spaced review that brings a topic back right before you'd forget it • Study Desk: a 2-minute micro-experiment every day, a Lab Notebook for your own conjectures, and a library of 219 counterexamples • A searchable library of 12 chapters, filterable by topic, tag and difficulty TOPICS COVERED • Limits and continuity • Derivatives and differentials • Applications of derivatives — optimization, related rates, MVT, curve sketching, L'Hôpital's rule, Taylor polynomials • Integrals — FTC, substitution, integration by parts, partial fractions, improper integrals • Applications of integration — area, volume, arc length, work • Differential equations • Infinite series — convergence tests, power series, Taylor and Fourier series • Multivariable differential calculus — partial derivatives, gradient, tangent planes, Lagrange multipliers • Vectors and 3D analytic geometry • Multiple integrals — double and triple integrals, cylindrical and spherical coordinates • Line and surface integrals — Green's, divergence and Stokes' theorems Great for Calculus I, II and III, AP Calculus AB/BC review, and exam prep. TRY IT FIRST Chapter 1 is completely free — animations, examples and practice all work, no time limit and no account. To unlock every chapter, choose Calculus Pro: a monthly or yearly auto-renewable subscription (the yearly plan may include a free trial for eligible users), or a one-time lifetime purchase. No ads. Works on iPhone, iPad and Mac. SUBSCRIPTION DETAILS Payment is charged to your Apple Account at confirmation of purchase. Subscriptions renew automatically unless cancelled at least 24 hours before the end of the current period. Manage or cancel anytime in Settings > Apple Account > Subscriptions. Prices are shown in the app before you buy. Your progress stays on your device. Purchases are handled securely by Apple and can be restored anytime. Every lesson, example and problem is available in English, Spanish, French, German, Italian, Portuguese, Japanese, Korean, Arabic, Hindi and Chinese. Privacy: https://vaca.vip/advancedmathematics/en/privacy Support: https://vaca.vip/advancedmathematics/en/support Terms of Use (EULA): https://www.apple.com/legal/internet-services/itunes/dev/stdeula/

Learn game theory and solve games step by step — with exact fractions, not rounded decimals. Game Theory: Nash Equilibrium is a course, a solver and a problem set in one app. Every answer comes with the reasoning behind it, so you can check your homework, prepare for an exam, or simply understand why people cooperate, compete and bluff. SOLVER — FOUR KINDS OF GAMES • Matrix games: 2 players with up to 6 strategies each, or 3 players with up to 3. Dominant strategies, iterated elimination, rationalizability, pure and mixed Nash equilibria, refinements, equilibrium selection, maximin, Pareto efficiency, Nash bargaining, Stackelberg commitment, repeated games, evolutionarily stable strategies and correlated equilibrium — 14 concepts in total. • Game trees: build a sequential game, add moves of chance, and solve it by backward induction. See which Nash equilibria rest on threats nobody would carry out. • Bayesian games: give one or both players private types and find the pure and mixed Bayesian Nash equilibria, checked type by type. • Cournot markets: 2 to 5 firms with known or private costs. Get best responses, the equilibrium, price, profits and consumer surplus, compared with a cartel, a Stackelberg leader and perfect competition — with the reaction curves drawn. LEARN — 24 TOPICS IN 6 UNITS From normal-form games and dominant strategies to mixed equilibria, subgame perfection, information sets, Bayesian games, signaling, auctions and continuous strategies. Each topic builds on the one before and includes a worked example computed by the same engine as the solver. PRACTICE — 31 CLASSIC PROBLEMS The Prisoner's Dilemma, Battle of the Sexes, Stag Hunt, Chicken, the tragedy of the commons, auctions, the Traveller's Dilemma and many more. Pick the equilibria yourself, get instant feedback, then study the full solution. WHY STUDENTS USE IT • Exact results: fractions such as 2/3 instead of 0.667, and all equilibria of two-player games, not just one. • Step by step: the method is shown, not only the answer. • 10 languages: English, Turkish, German, Spanish, French, Italian, Portuguese, Russian, Chinese and Japanese. • Lessons, solver and practice work offline (watching an ad needs a connection). No account, no tracking, no banners. FREE TO TRY, ONE PURCHASE FOR EVERYTHING Lessons 1, 2 and 24 and two practice problems (the Prisoner's Dilemma and Chicken, with their solutions) are free, and so is the solver: without Full Access, each solve is unlocked by one short ad that you choose to watch. Full Access — a one-time in-app purchase, not a subscription — unlocks every lesson, ad-free solving and all 31 problems with their solutions. Made for students of economics, business, computer science and political science, in high school and at university, and for anyone curious about strategic thinking.