SE PRESENTA UN ENFOQUE ACTUALIZADO Y DIDÁCTICO PARA LAS FUNCIONES DE MATHIEU COMO UNA ALTERNATIVA A LA PRESENTACIÓN ORTODOXA. LA EVALUACIÓN MATRICIAL DE LAS FUNCIONES DE MATHIEU ANGULARES ES NO SOLAMENTE PERTINENTE SINO RETRASADA DESPUÉS DE SETENTA Y CINCO AÑOS DE MECÁNICA CUÁNTICA MATRICIAL Y CON LA DISPONIBILIDAD DE HERRAMIENTAS COMPUTACIONALES. SE IDENTIFICAN LAS ONDAS PLANAS COMO FUNCIONES GENERADORAS DE LAS FUNCIONES DE MATHIEU, MOSTRANDO SUS DESARROLLOS EXPLÍCITOS. SE ILUSTRAN ALGUNAS APLICACIONES MATEMÁTICAS Y FÍSICAS.AbstractAN UPDATED DIDACTICAL APPROACH TO MATHIEU FUNCTIONS IS PRESENTED AS AN ALTERNATIVE TO THE ORTHODOX TREATMENT. THE MATRIX EVALUATION OF THE ANGULAR MATHIEU FUNCTIONS IS NOT ONLY PERTINENT, BUT LONG OVER DUE, AFTER SEVENTY FIVE YEARS OF MATRIX QUANTUM MECHANICS AND WITH THE AVAILABILITY OF COMPUTING TOOLS. PLANE WAVES ARE IDENTIFIED AS GENERATING FUNCTIONS OF THE MATHIEU FUNCTIONS, SHOWING THEIR EXPLICIT EXPANSIONS. SOME MATHEMATICAL AND PHYSICAL APPLICATIONS ARE ILLUSTRATED.AN UPDATED DIDACTICAL APPROACH TO MATHIEU FUNCTIONS IS PRESENTED AS AN ALTERNATIVE TO THE ORTHODOX TREATMENT. THE MATRIX EVALUATION OF THE ANGULAR MATHIEU FUNCTIONS IS NOT ONLY PERTINENT, BUT LONG OVER DUE, AFTER SEVENTY FIVE YEARS OF MATRIX QUANTUM MECHANICS AND WITH THE AVAILABILITY OF COMPUTING TOOLS. PLANE WAVES ARE IDENTIFIED AS GENERATING FUNCTIONS OF THE MATHIEU FUNCTIONS, SHOWING THEIR EXPLICIT EXPANSIONS. SOME MATHEMATICAL AND PHYSICAL APPLICATIONS ARE ILLUSTRATED.